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Iranian Journal of Physics Research

Berry phase for a particle in an infinite spherical potential well with moving wall

Reza Moazzemi

Published Jun 1, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.29252/ijpr.19.1.25

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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.
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.
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.