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Modern Physics Letters B

Berry phase in a quantum system with time-dependent boundary conditions

Anling Wang, Fuping Liu, Zhao-Xian Yu

Published Jun 17, 2014• 2 citations
Publisher

Abstract

We discuss the problem of the quantum particle behavior in an infinitely deep elliptical potential well with a moving boundary conditions. We show that this quantum system is equivalent to a particle interacting with a vector field. By introducing the squeezing transformations and making use of the removability of the topological term, the exact Berry phase in a cyclic evolution is calculated.

DOI
10.1142/s021798491450122x

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THE BERRY PHASE OF THE QUANTUM STATE OF A HARMONIC OSCILLATOR WITH TIME-DEPENDENT FREQUENCY AND BOUNDARY CONDITIONS

Liu Deng-yun, 山西师范大学物理系，临汾 041004

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.

Acta Physica Sinica•Jan 1, 1998•2 citations
We discuss the problem of the quantum particle behavior in an infinitely deep elliptical potential well with a moving boundary conditions. We show that this quantum system is equivalent to a particle interacting with a vector field. By introducing the squeezing transformations and making use of the removability of the topological term, the exact Berry phase in a cyclic evolution is calculated.
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.
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 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.
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.