In this paper we find that a set of energy eigenstates of a two-dimensional anisotropic harmonic potential in a uniform magnetic field is classified as the atomic coherent states ｜τ） in terms of the spin values of ...In this paper we find that a set of energy eigenstates of a two-dimensional anisotropic harmonic potential in a uniform magnetic field is classified as the atomic coherent states ｜τ） in terms of the spin values of j in the Schwinger bosonic realization. The correctness of the above conclusions can be verified by virtue of the entangled state 〈η｜ representation of the state ｜τ）.展开更多
The notes here presented are of the modifications introduced in the application of WKB method.Theproblems of two-and three-dimensional harmonic oscillator potential are revisited by WKB and the new formulationof quant...The notes here presented are of the modifications introduced in the application of WKB method.Theproblems of two-and three-dimensional harmonic oscillator potential are revisited by WKB and the new formulationof quantization rule respectively.It is found that the energy spectrum of the radial harmonic oscillator,which isreproduced exactly by the standard WKB method with the Langer modification,is also reproduced exactly without theLanger modification via the new quantization rule approach.An alternative way to obtain the non-integral Maslov indexfor three-dimensional harmonic oscillator is proposed.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 10574060)the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)the Shandong Provincal Higher Educational Science and Technology Program of China (Grant Nos. J09LA07 and J10LA15)
文摘In this paper we find that a set of energy eigenstates of a two-dimensional anisotropic harmonic potential in a uniform magnetic field is classified as the atomic coherent states ｜τ） in terms of the spin values of j in the Schwinger bosonic realization. The correctness of the above conclusions can be verified by virtue of the entangled state 〈η｜ representation of the state ｜τ）.
基金National Natural Science Foundation of China under Grant No.10747130the Foundation of East China University of Science and Technology
文摘The notes here presented are of the modifications introduced in the application of WKB method.Theproblems of two-and three-dimensional harmonic oscillator potential are revisited by WKB and the new formulationof quantization rule respectively.It is found that the energy spectrum of the radial harmonic oscillator,which isreproduced exactly by the standard WKB method with the Langer modification,is also reproduced exactly without theLanger modification via the new quantization rule approach.An alternative way to obtain the non-integral Maslov indexfor three-dimensional harmonic oscillator is proposed.
