We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground...We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.展开更多
A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The p...A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The proposed method,based on the optimized multi-index modulation, does not limit the number of signals in the first and second constellations and abandons the concept of limiting the number of signals in different constellations. It successfully increases the spectrum efficiency of the system while expanding the number of modulation symbol combinations and the index dimension of PSWFs signals. The proposed method outperforms the PSWFs multi-carrier index modulation method based on optimized multiple indexes in terms of spectrum efficiency, but at the expense of system computational complexity and bit error performance. For example, with n=10 subcarriers and a bit error rate of 1×10^(-5),spectral efficiency can be raised by roughly 12.4%.展开更多
To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the tim...To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found.展开更多
The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first tr...The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first transformed into the time independent one. And then exact wave function is found in terms of solutions of the classical equation of motion of the oscillator.展开更多
The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential t...The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.展开更多
The antisymmetrized geminal power (AGP) and sequential product of geminals(SPG) functions, the basis functions with symplectic symmetry, are linearly combined to calculate the ground state of the LiH molecule. The cal...The antisymmetrized geminal power (AGP) and sequential product of geminals(SPG) functions, the basis functions with symplectic symmetry, are linearly combined to calculate the ground state of the LiH molecule. The calculation results show that the AGP or SPG function gives the same ground state results as the linear combination.展开更多
By using a trial wave function,the exact wave function for a harmonic oscillator with time-dependent mass,frequency,damping and driving is obtained.And then by defining a unitary operator,coherent states for the syste...By using a trial wave function,the exact wave function for a harmonic oscillator with time-dependent mass,frequency,damping and driving is obtained.And then by defining a unitary operator,coherent states for the system of interest are found.These coherent states have most,but not all,of the properties the time independent oscillator.And all the results obtained can be reduced to the usual ones when both the mass and fre-quency are constants and the driving is absent.展开更多
The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the ap...The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the appearance of the imaginary unit in quantum mechanics and introduces clear definition of wave functions. When a wave function acts through the Hopf fibration on a localized geometric algebra element, that is executing a measurement, the result can be named as “collapse” of the wave function.展开更多
Shortcomings of the Boltzmann physical kinetics and the Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger wave mechanics are considered. From the position of nonlocal p...Shortcomings of the Boltzmann physical kinetics and the Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger wave mechanics are considered. From the position of nonlocal physics, the Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger equation is a local equation;this fact leads to the great shortcomings of the linear Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger wave mechanics. Nonlocal nonlinear quantum mechanics is considered using the wave function terminology.展开更多
Based on the electron dynamic diffraction, phase shift of the exit wave function vs misorientation of the incident electron beam from the exact zone axis has been calculated for the [001] oriented copper. The result s...Based on the electron dynamic diffraction, phase shift of the exit wave function vs misorientation of the incident electron beam from the exact zone axis has been calculated for the [001] oriented copper. The result shows that the peak of phase shift is the maximum at the atom position as the electron beam along the exact [001] zone axis, and the peak value of phase shift decreases as increases of the misorientation. At small misorientation, i.e. less than 5 degree, change of the phase shift is minimal. The peak value of phase shift decreases significantly when the incident beam deviates form the zone axis over 10 degree and the exit wave has a planar configuration as the misoriention angle arrives -17 degree. The effect of this phase shift characteristics on the information extracted from the hologram has also been considered.展开更多
We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）...We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）]｜0 in the coordinate representation. A new operator＇s disentangling formula is derived as a by-product.展开更多
Time evaluation of wave functions for any quantum mechanical system/particle is essential nevertheless quantum mechanical counterpart of the time dependant classical wave equation does simply not appear. Epistemologic...Time evaluation of wave functions for any quantum mechanical system/particle is essential nevertheless quantum mechanical counterpart of the time dependant classical wave equation does simply not appear. Epistemologically and ontologically considered time dependant momentum operator is initially defined and an Alternative Time Dependant Schrodinger Wave Equation (ATDSWE) is plainly derived. Consequent equation is primarily solved for the free particles, in a closed system, signifying a good agreement with the outcomes of the ordinary TDSWE. Free particle solution interestingly goes further possibly tracing some signs of new pathways to resolve the mysterious quantum world.展开更多
The properties of muonic helium atom （^4He＋2μ-e-） in ground state are considered. In this work, the energy and average distance between particles have been obtained using a wave function, which satisfies boundary ...The properties of muonic helium atom （^4He＋2μ-e-） in ground state are considered. In this work, the energy and average distance between particles have been obtained using a wave function, which satisfies boundary conditions. It is shown that the obtained energy are very close to the values calculated by others. But the small differences of the expectation values of r^2n are due to the incorporated boundary conditions in proposed wave function and are expected.展开更多
For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functio...For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.展开更多
The effect of final-state dynamic correlation is investigated for ionization of atomic hydrogen by 75-keV proton impact by analyzing double differential cross sections.The final state is represented by a continuum cor...The effect of final-state dynamic correlation is investigated for ionization of atomic hydrogen by 75-keV proton impact by analyzing double differential cross sections.The final state is represented by a continuum correlated wave(CCW-PT)function which accounts for the interaction between the projectile and the target nucleus(PT interaction).The correlated final state is nonseparable solutions of the wave equation combining the dynamics of the electron motion relative to the target and projectile,satisfying the Redmond’s asymptotic conditions corresponding to long range interactions.The transition matrix is evaluated using the CCW-PT function and the undistorted initial state.Both the correlation effects and the PT interaction are analyzed by the present calculations.The convergence of the continuous correlated final state is examined carefully.Our results are compared with the absolute experimental data measured by Laforge et al.[Phys.Rev.Lett.103,053201(2009)]and Schulz et al.[Phys.Rev.A 81,052705(2010)],as well as other theoretical models(especially the results of the latest non perturbation theory).We have shown that the dynamic correlation plays an important role in the ionization of atomic hydrogen by proton impact.While overall agreement between theory and the experimental data is encouraging,detailed agreement is still lacking.However,such an analysis is meaningful because it provides valuable information about the dynamical correlation and PT interaction in the CCW-PT theoretical model.展开更多
The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.
We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential.It is found that,in the presence of a Coulomb potential of type I(with three equal diagonal elements),similarly to ...We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential.It is found that,in the presence of a Coulomb potential of type I(with three equal diagonal elements),similarly to that in the twodimensional case,the flat band could not survive.At the same time,the flat band states are transformed into localized states with a logarithmic singularity near the center position.In addition,the wave function near the origin would collapse for an arbitrarily weak Coulomb potential.Due to the wave function collapses,the eigen-energies for a shifted Coulomb potential depend sensitively on the cut-off parameter.For a Coulomb potential of type II,there exist infinite bound states that are generated from the flat band.Furthermore,when the bound state energy is very near the flat band,the energy is inversely proportional to the natural number,e.g.,E_(n)∝1/n,n=1,2,3,...It is expected that the 1/n energy spectrum could be observed experimentally in the near future.展开更多
We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlat...We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlation energy, and first-order wave function are divided into two components, one component associated with the repulsive coulomb interaction and the other proportional to magnetic shielding. The resulting first-order wave functions are applied to calculate second-order energies within the model. We find that the second-order energies are independent of the nuclear charge screening constant in the unperturbed Hamiltonian with a central coulomb potential.展开更多
By using the linear combination of the AGP(antisymmetrtzed geminat power) and SPG(sequential product of geminats) functions, an attempt has been made to catcutate the ground state of the LiH molecule. The calculated r...By using the linear combination of the AGP(antisymmetrtzed geminat power) and SPG(sequential product of geminats) functions, an attempt has been made to catcutate the ground state of the LiH molecule. The calculated results show that-the AGP or SPG function gives the same ground state result as their linear combination.展开更多
The multiverse is a hypothesis created to solve certain problems in cosmology. Currently, this scheme is still largely ad hoc, rather than derived from fundamental laws and principles. Because of this, the predictive ...The multiverse is a hypothesis created to solve certain problems in cosmology. Currently, this scheme is still largely ad hoc, rather than derived from fundamental laws and principles. Because of this, the predictive power of this theory is rather limited. Furthermore, there are concerns that this theory will make it impossible to calculate some measured quantities, such as the masses of quarks and the electron. In this paper, we will show that a new development in string theory, the universal wave function interpretation of string theory, provides a way to derive the mathematical expression of the multiverse. We will demonstrate that the Weyl invariance existing in string theory indicates that our observed universe is a projection from a hologram. We will present how the laws of physics can be derived from this fact. Furthermore, we suggest it may also provide a way to calculate the masses of fundamental particles such as quarks and the electron.展开更多
基金supported by the National Key R&D Program of China(No.2023YFA1606701)the National Natural Science Foundation of China(Nos.12175042,11890710,11890714,12047514,12147101,and 12347106)+1 种基金Guangdong Major Project of Basic and Applied Basic Research(No.2020B0301030008)China National Key R&D Program(No.2022YFA1602402).
文摘We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.
基金supported by the China National Postdoctoral Program for Innovative Talents(BX20200039)the Special Fund Project of“Mount Taishan Scholars”Construction Project in Shandong Province(ts20081130).
文摘A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The proposed method,based on the optimized multi-index modulation, does not limit the number of signals in the first and second constellations and abandons the concept of limiting the number of signals in different constellations. It successfully increases the spectrum efficiency of the system while expanding the number of modulation symbol combinations and the index dimension of PSWFs signals. The proposed method outperforms the PSWFs multi-carrier index modulation method based on optimized multiple indexes in terms of spectrum efficiency, but at the expense of system computational complexity and bit error performance. For example, with n=10 subcarriers and a bit error rate of 1×10^(-5),spectral efficiency can be raised by roughly 12.4%.
文摘To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found.
基金National Natural Science Foundation (K19972 0 11)
文摘The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first transformed into the time independent one. And then exact wave function is found in terms of solutions of the classical equation of motion of the oscillator.
基金the National Natural Science Foundation of China under Grand No.549974011
文摘The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.
文摘The antisymmetrized geminal power (AGP) and sequential product of geminals(SPG) functions, the basis functions with symplectic symmetry, are linearly combined to calculate the ground state of the LiH molecule. The calculation results show that the AGP or SPG function gives the same ground state results as the linear combination.
基金Spomsored by the National Natural Science Foundation(K19972011)
文摘By using a trial wave function,the exact wave function for a harmonic oscillator with time-dependent mass,frequency,damping and driving is obtained.And then by defining a unitary operator,coherent states for the system of interest are found.These coherent states have most,but not all,of the properties the time independent oscillator.And all the results obtained can be reduced to the usual ones when both the mass and fre-quency are constants and the driving is absent.
文摘The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the appearance of the imaginary unit in quantum mechanics and introduces clear definition of wave functions. When a wave function acts through the Hopf fibration on a localized geometric algebra element, that is executing a measurement, the result can be named as “collapse” of the wave function.
文摘Shortcomings of the Boltzmann physical kinetics and the Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger wave mechanics are considered. From the position of nonlocal physics, the Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger equation is a local equation;this fact leads to the great shortcomings of the linear Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger wave mechanics. Nonlocal nonlinear quantum mechanics is considered using the wave function terminology.
基金financially supported tional Natural Science Foundation of China No. 60271028.
文摘Based on the electron dynamic diffraction, phase shift of the exit wave function vs misorientation of the incident electron beam from the exact zone axis has been calculated for the [001] oriented copper. The result shows that the peak of phase shift is the maximum at the atom position as the electron beam along the exact [001] zone axis, and the peak value of phase shift decreases as increases of the misorientation. At small misorientation, i.e. less than 5 degree, change of the phase shift is minimal. The peak value of phase shift decreases significantly when the incident beam deviates form the zone axis over 10 degree and the exit wave has a planar configuration as the misoriention angle arrives -17 degree. The effect of this phase shift characteristics on the information extracted from the hologram has also been considered.
基金Project supported by the National Natural Science Foundation of China(Grant No.11175113)
文摘We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）]｜0 in the coordinate representation. A new operator＇s disentangling formula is derived as a by-product.
文摘Time evaluation of wave functions for any quantum mechanical system/particle is essential nevertheless quantum mechanical counterpart of the time dependant classical wave equation does simply not appear. Epistemologically and ontologically considered time dependant momentum operator is initially defined and an Alternative Time Dependant Schrodinger Wave Equation (ATDSWE) is plainly derived. Consequent equation is primarily solved for the free particles, in a closed system, signifying a good agreement with the outcomes of the ordinary TDSWE. Free particle solution interestingly goes further possibly tracing some signs of new pathways to resolve the mysterious quantum world.
文摘The properties of muonic helium atom （^4He＋2μ-e-） in ground state are considered. In this work, the energy and average distance between particles have been obtained using a wave function, which satisfies boundary conditions. It is shown that the obtained energy are very close to the values calculated by others. But the small differences of the expectation values of r^2n are due to the incorporated boundary conditions in proposed wave function and are expected.
基金supported by the National Key R and D Program of China(2020YFA0713100).
文摘For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11974229 and 11274215)。
文摘The effect of final-state dynamic correlation is investigated for ionization of atomic hydrogen by 75-keV proton impact by analyzing double differential cross sections.The final state is represented by a continuum correlated wave(CCW-PT)function which accounts for the interaction between the projectile and the target nucleus(PT interaction).The correlated final state is nonseparable solutions of the wave equation combining the dynamics of the electron motion relative to the target and projectile,satisfying the Redmond’s asymptotic conditions corresponding to long range interactions.The transition matrix is evaluated using the CCW-PT function and the undistorted initial state.Both the correlation effects and the PT interaction are analyzed by the present calculations.The convergence of the continuous correlated final state is examined carefully.Our results are compared with the absolute experimental data measured by Laforge et al.[Phys.Rev.Lett.103,053201(2009)]and Schulz et al.[Phys.Rev.A 81,052705(2010)],as well as other theoretical models(especially the results of the latest non perturbation theory).We have shown that the dynamic correlation plays an important role in the ionization of atomic hydrogen by proton impact.While overall agreement between theory and the experimental data is encouraging,detailed agreement is still lacking.However,such an analysis is meaningful because it provides valuable information about the dynamical correlation and PT interaction in the CCW-PT theoretical model.
文摘The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.
基金the supports of startup grant from Guangzhou Universitysupported by the National Natural Science Foundation of China(Grant No.11874127)。
文摘We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential.It is found that,in the presence of a Coulomb potential of type I(with three equal diagonal elements),similarly to that in the twodimensional case,the flat band could not survive.At the same time,the flat band states are transformed into localized states with a logarithmic singularity near the center position.In addition,the wave function near the origin would collapse for an arbitrarily weak Coulomb potential.Due to the wave function collapses,the eigen-energies for a shifted Coulomb potential depend sensitively on the cut-off parameter.For a Coulomb potential of type II,there exist infinite bound states that are generated from the flat band.Furthermore,when the bound state energy is very near the flat band,the energy is inversely proportional to the natural number,e.g.,E_(n)∝1/n,n=1,2,3,...It is expected that the 1/n energy spectrum could be observed experimentally in the near future.
文摘We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlation energy, and first-order wave function are divided into two components, one component associated with the repulsive coulomb interaction and the other proportional to magnetic shielding. The resulting first-order wave functions are applied to calculate second-order energies within the model. We find that the second-order energies are independent of the nuclear charge screening constant in the unperturbed Hamiltonian with a central coulomb potential.
基金Supported by the National Natural Science Foundation of China
文摘By using the linear combination of the AGP(antisymmetrtzed geminat power) and SPG(sequential product of geminats) functions, an attempt has been made to catcutate the ground state of the LiH molecule. The calculated results show that-the AGP or SPG function gives the same ground state result as their linear combination.
文摘The multiverse is a hypothesis created to solve certain problems in cosmology. Currently, this scheme is still largely ad hoc, rather than derived from fundamental laws and principles. Because of this, the predictive power of this theory is rather limited. Furthermore, there are concerns that this theory will make it impossible to calculate some measured quantities, such as the masses of quarks and the electron. In this paper, we will show that a new development in string theory, the universal wave function interpretation of string theory, provides a way to derive the mathematical expression of the multiverse. We will demonstrate that the Weyl invariance existing in string theory indicates that our observed universe is a projection from a hologram. We will present how the laws of physics can be derived from this fact. Furthermore, we suggest it may also provide a way to calculate the masses of fundamental particles such as quarks and the electron.
