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Acta Physica Sinica

HAMILTONIAN OPERATORS CONSTRUCTED FROM TWO KINDS OF FINITE-DEPTH QUANTUM POTENTIAL WELLS WITH TIME-DEPENDENT BOUNDARY CONDITIONS AND THEIR COMPLEX BERRY PHASES

ZHANG RUN-DONG, Yan Feng-Li, Bo‐Zang Li, (1)河北师范大学物理系，石家庄 050016; (2)中国科学院物理研究所和凝聚态物理中心，北京 100080

Published Jan 1, 1998• 1 citation
Publisher

Abstract

In the frame of the basic quantum theory,from the one-dimensional infinite-height half-wall quantum potential well with time-dependent boundary conditions and from the three-dimensional finite-depth sphere-square potential well with time-dependent boundary conditions we constructed two kinds of new Hamiltonian operators separately which describe electric particle interacting with eletromagnetic field.In the adiabatic approximation are calculated the complex Berry phases of two kinds of new systems.

DOI
10.7498/aps.47.1585

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In the frame of the basic quantum theory,from the one-dimensional infinite-height half-wall quantum potential well with time-dependent boundary conditions and from the three-dimensional finite-depth sphere-square potential well with time-dependent boundary conditions we constructed two kinds of new Hamiltonian operators separately which describe electric particle interacting with eletromagnetic field.In the adiabatic approximation are calculated the complex Berry phases of two kinds of new systems.
AbstractIn the frame of the basic quantum theory,from the one dimensional infinite height half wall quantum potential well with time dependent boundary conditions and from the three dimensional finite depth sphere square potential well with time dependent boundary conditions we constructed two kinds of new Hamiltonian operators separately which describe electric particle interacting with eletromagnetic field.In the adiabatic approximation are calculated the complex Berry phases of two kinds of new systems.
For a quantum system with time dependent boundary conditions, it is shown that the ef-fective Hamiltonian can be constructed in a simple way without any geometric treatemnt. In this paper the effective Hamiltonian, constructed in the above way, of quantum particle in a spherical box of varying radius is used to calculate the Berry phase of the wave function. We found that the effective Hamiltonian and original one are formally related with a static gauge transformation, the quantum states of the two Hamiltonians differ by a Berry phase.
The problem of a harmonic oscillator of time-dependent frequency confined in a one-dimensional infinite square well with a moving wall is studied.It is shown that the exact solution and the Lewis invariant operator of the system can be obtained by performing two consecutive gauge transformations on the time-dependent Schrdinger equation.On the basis of the exact solution the Berry phases for the system are calculated by using the geometric concepts such as the geometric distance and geometric length of the curve.
Abstract The problem of a harmonic oscillator of time dependent frequency confined in a one dimensional infinite square well with a moving wall is studied.It is shown that the exact solution and the Lewis invariant operator of the system can be obtained by performing two consecutive gauge transformations on the time dependent Schrdinger equation.On the basis of the exact solution the Berry phases for the system are calculated by using the geometric concepts such as the geometric distance and geometric length of the curve.
In this paper we calculate the Berry phase for a wave function of a particle in an infinite spherical potential well with adiabatically varying. In order to do this, we need the solutions of the corresponding Schrödinger equation with a time dependent Hamiltonian. Here, we obtain these solutions for the first time. In addition, we calculate the Berry phase in one dimensional case for an infinite potential well. We see that this phase is comparable with the usual dynamical phase but with different sign. Therefore, it is important to take it into account in the quantum mechanical calculations.