We use the invariant eigen-operator method to study the higher-dimensional harmonic oscillator in a type of generalized noncommutative phase space,and obtain the explicit expression of the energy spectra of the noncom...We use the invariant eigen-operator method to study the higher-dimensional harmonic oscillator in a type of generalized noncommutative phase space,and obtain the explicit expression of the energy spectra of the noncommutative harmonic oscillator in arbitrary dimension.It is found that the energy spectra of the higher-dimensional noncommutative harmonic oscillator are equal to the sum of the energy spectra of some 1D harmonic oscillators and some 2D noncommutative harmonic oscillators.We believe that the properties of the harmonic oscillator may reflect some essence of the noncommutative phase space.展开更多
In this paper,we investigate the categorical description of the boson oscillator.Based on the categories constructed by Khovanov,we introduce a categorification of the Fock states and the corresponding inner product o...In this paper,we investigate the categorical description of the boson oscillator.Based on the categories constructed by Khovanov,we introduce a categorification of the Fock states and the corresponding inner product of these states.We find that there are two different categorical definitions of the inner product of the Fock states.These two definitions are consistent with each other,and the decategorification results also coincide with those in conventional quantum mechanics.We also find that there are some interesting properties of the 2-morphisms which relate to the inner product of the states.展开更多
In this paper, we study the diagrammatic categorification of q-boson algebra and also q-fermion algebra. We construct a graphical category corresponding to q-boson algebra, q-Fock states correspond to some kind of 1-m...In this paper, we study the diagrammatic categorification of q-boson algebra and also q-fermion algebra. We construct a graphical category corresponding to q-boson algebra, q-Fock states correspond to some kind of 1-morphisms, and the graded dimension of the graded vector space of 2-morphisms is exactly the inner product of the corresponding q-Fock states. We also find that this graphical category can be used to categorify q-fermion algebra.展开更多
基金by the Talented Person Troop Items of Basic Construction of Anhui University.
文摘We use the invariant eigen-operator method to study the higher-dimensional harmonic oscillator in a type of generalized noncommutative phase space,and obtain the explicit expression of the energy spectra of the noncommutative harmonic oscillator in arbitrary dimension.It is found that the energy spectra of the higher-dimensional noncommutative harmonic oscillator are equal to the sum of the energy spectra of some 1D harmonic oscillators and some 2D noncommutative harmonic oscillators.We believe that the properties of the harmonic oscillator may reflect some essence of the noncommutative phase space.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10975102,10871135,11031005,11075014
文摘In this paper,we investigate the categorical description of the boson oscillator.Based on the categories constructed by Khovanov,we introduce a categorification of the Fock states and the corresponding inner product of these states.We find that there are two different categorical definitions of the inner product of the Fock states.These two definitions are consistent with each other,and the decategorification results also coincide with those in conventional quantum mechanics.We also find that there are some interesting properties of the 2-morphisms which relate to the inner product of the states.
基金supported by the National Natural Science Foundation of China (Grant Nos.10975102,10871135,11031005,and 11075014)
文摘In this paper, we study the diagrammatic categorification of q-boson algebra and also q-fermion algebra. We construct a graphical category corresponding to q-boson algebra, q-Fock states correspond to some kind of 1-morphisms, and the graded dimension of the graded vector space of 2-morphisms is exactly the inner product of the corresponding q-Fock states. We also find that this graphical category can be used to categorify q-fermion algebra.
