We study the Hcisenberg moder under the influence of a rotating magnetic field. By using a time- dependent unitary transformation, the time evolution operator for the Schrodinger equation is obtained, which involves n...We study the Hcisenberg moder under the influence of a rotating magnetic field. By using a time- dependent unitary transformation, the time evolution operator for the Schrodinger equation is obtained, which involves no chronological product. The spin vectors (mean values of the spin operators) are obtained as explicit functions of time in the most general case. A series of cyclic solutions are presented. The nonadiabatic geometric phases of these cyclic solutions are caleulated, and are expressed in terms of the solid angle subtended by the closed trace of thc total spin vector, as well as in terms of those of the individual spins.展开更多
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied.Several configurations of the electromagnetic field are considered.T...A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied.Several configurations of the electromagnetic field are considered.The Schoedinger equation is solved analytically in most of the cases.The energy levels and wave functions are obtained explicitly.In some of the cases,the ground state obtained is not a minimum wave packet,though it is of the Gaussian type.Coherent and squeezed states and their time evolution are discussed in detail.展开更多
文摘We study the Hcisenberg moder under the influence of a rotating magnetic field. By using a time- dependent unitary transformation, the time evolution operator for the Schrodinger equation is obtained, which involves no chronological product. The spin vectors (mean values of the spin operators) are obtained as explicit functions of time in the most general case. A series of cyclic solutions are presented. The nonadiabatic geometric phases of these cyclic solutions are caleulated, and are expressed in terms of the solid angle subtended by the closed trace of thc total spin vector, as well as in terms of those of the individual spins.
文摘A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied.Several configurations of the electromagnetic field are considered.The Schoedinger equation is solved analytically in most of the cases.The energy levels and wave functions are obtained explicitly.In some of the cases,the ground state obtained is not a minimum wave packet,though it is of the Gaussian type.Coherent and squeezed states and their time evolution are discussed in detail.
