A pair of up-down operators are constructed explicitly for S.C.Zhang's SO(5) theory of high Tc superconductivity.From them two good quantum numbers are derived.The up-down operators are related to the spin-indepen...A pair of up-down operators are constructed explicitly for S.C.Zhang's SO(5) theory of high Tc superconductivity.From them two good quantum numbers are derived.The up-down operators are related to the spin-independent excitons which are not considered before.展开更多
A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximat...A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.展开更多
The effective one-body(EOB) theory provides an innovative framework for analyzing the dynamics of binary systems, as articulated by Hamilton's equations. This paper investigates a self-consistent EOB theory specif...The effective one-body(EOB) theory provides an innovative framework for analyzing the dynamics of binary systems, as articulated by Hamilton's equations. This paper investigates a self-consistent EOB theory specifically tailored for the dynamics of such systems. Our methodology begins by emphasizing how to effectively utilize the metrics derived from scattering angles in the analysis of binary black hole mergers. We then construct an effective Hamiltonian and formulate a decoupled, variableseparated Teukolsky-like equation for ψ_(4)^(B). Furthermore, we present the formal solution to this equation, detailing the energy flux, radiation-reaction force(RRF), and waveforms for the “plus” and “cross” modes generated by spinless binaries. Finally, we carry out numerical calculations using the EOB theory and compare the results with numerical relativity(NR) data from the SXS collaboration. The results indicate that to the innermost stable circular orbit, the binding energy-angular momentum relation differs from the NR results by less than 5‰, with a larger mass ratio yielding better agreement.展开更多
By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter （SS） equation with the Woods-Saxon interaction pote...By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter （SS） equation with the Woods-Saxon interaction potential for an arbitrary/-state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied： the approximated SchrSdinger- Woods-Saxon problem for an arbitrary/-state and the exact s-wave （l=0）.展开更多
The exact solution of Spinless-Salpeter equation （SSE） in the presence of Kink-Like potential is in-vestigated. By using the basic concepts of the supersyrnmetric quantum mechanics （SUSYQM） formalism and the funct...The exact solution of Spinless-Salpeter equation （SSE） in the presence of Kink-Like potential is in-vestigated. By using the basic concepts of the supersyrnmetric quantum mechanics （SUSYQM） formalism and the functional analysis method, we have obtained the bound state solutions in the closed form and the eigenfunctions of the system are reported in the term of hypergeometric function. We have also reported some numerical results.展开更多
The two-body Spinless Salpeter equation for the Woods-Saxon potential is solved by using the super- symmetry quantum mechanics （SUSYQM）. In our calculations, we have applied an approximation to the centrifugal barri...The two-body Spinless Salpeter equation for the Woods-Saxon potential is solved by using the super- symmetry quantum mechanics （SUSYQM）. In our calculations, we have applied an approximation to the centrifugal barrier. Energy eigenvalues and the corresponding eigenfunctions are computed for various values of quantum numbers n, I.展开更多
Scattering solutions of two-body Spinless Salpeter Equation(SSE) are investigated in the center of mass frame with a repulsive, symmetric Hulth′en potential in one spatial dimension. Transmission and reflection coeff...Scattering solutions of two-body Spinless Salpeter Equation(SSE) are investigated in the center of mass frame with a repulsive, symmetric Hulth′en potential in one spatial dimension. Transmission and reflection coefficients are calculated and discussed.展开更多
We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation （SSE） with the Yukawa potential via the supersymmetric quantum mechanics （SUSYQM） for arbitrary quantum numbers. ...We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation （SSE） with the Yukawa potential via the supersymmetric quantum mechanics （SUSYQM） for arbitrary quantum numbers. Useful figures and tables are also included.展开更多
In this paper we have solved the two-body spinless-Salpeter（SS） equation under the Coulomb and exponential type potentials. We have applied an approximation for the centrifugal term in our calculations. The energy e...In this paper we have solved the two-body spinless-Salpeter（SS） equation under the Coulomb and exponential type potentials. We have applied an approximation for the centrifugal term in our calculations. The energy eigenvalues and the corresponding eigenfunctions are reported by using the Laplace transform approach for any n, states.展开更多
文摘A pair of up-down operators are constructed explicitly for S.C.Zhang's SO(5) theory of high Tc superconductivity.From them two good quantum numbers are derived.The up-down operators are related to the spin-independent excitons which are not considered before.
文摘A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.
基金supported by the National Natural Science Foundation of China(Grant Nos.12035005,and 12475051)the National Key Research and Development Program of China(Grant No.2020YFC2201400).
文摘The effective one-body(EOB) theory provides an innovative framework for analyzing the dynamics of binary systems, as articulated by Hamilton's equations. This paper investigates a self-consistent EOB theory specifically tailored for the dynamics of such systems. Our methodology begins by emphasizing how to effectively utilize the metrics derived from scattering angles in the analysis of binary black hole mergers. We then construct an effective Hamiltonian and formulate a decoupled, variableseparated Teukolsky-like equation for ψ_(4)^(B). Furthermore, we present the formal solution to this equation, detailing the energy flux, radiation-reaction force(RRF), and waveforms for the “plus” and “cross” modes generated by spinless binaries. Finally, we carry out numerical calculations using the EOB theory and compare the results with numerical relativity(NR) data from the SXS collaboration. The results indicate that to the innermost stable circular orbit, the binding energy-angular momentum relation differs from the NR results by less than 5‰, with a larger mass ratio yielding better agreement.
文摘By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter （SS） equation with the Woods-Saxon interaction potential for an arbitrary/-state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied： the approximated SchrSdinger- Woods-Saxon problem for an arbitrary/-state and the exact s-wave （l=0）.
文摘The exact solution of Spinless-Salpeter equation （SSE） in the presence of Kink-Like potential is in-vestigated. By using the basic concepts of the supersyrnmetric quantum mechanics （SUSYQM） formalism and the functional analysis method, we have obtained the bound state solutions in the closed form and the eigenfunctions of the system are reported in the term of hypergeometric function. We have also reported some numerical results.
文摘The two-body Spinless Salpeter equation for the Woods-Saxon potential is solved by using the super- symmetry quantum mechanics （SUSYQM）. In our calculations, we have applied an approximation to the centrifugal barrier. Energy eigenvalues and the corresponding eigenfunctions are computed for various values of quantum numbers n, I.
文摘Scattering solutions of two-body Spinless Salpeter Equation(SSE) are investigated in the center of mass frame with a repulsive, symmetric Hulth′en potential in one spatial dimension. Transmission and reflection coefficients are calculated and discussed.
文摘We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation （SSE） with the Yukawa potential via the supersymmetric quantum mechanics （SUSYQM） for arbitrary quantum numbers. Useful figures and tables are also included.
文摘In this paper we have solved the two-body spinless-Salpeter（SS） equation under the Coulomb and exponential type potentials. We have applied an approximation for the centrifugal term in our calculations. The energy eigenvalues and the corresponding eigenfunctions are reported by using the Laplace transform approach for any n, states.
