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

Moazzemi, R

doi:10.29252/ijpr.19.1.25

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

Author

R Moazzemi

https://doi.org/10.29252/ijpr.19.1.25

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.

Keywords

Berry phase

geometrical phase

infinite spherical potential well

1. M V Berry, Proc. R. Soc. London A 392 (1984) 45.
2. A Bohm, A Mostafazadeh, H Koizumi, Q Niu, and J Zwanziger, “The Geometric Phase in Quantum Systems: Foundations, Mathematical Concepts, and Applications in Molecular and Condensed Matter Physics”, Springer-Verlag, Berlin (2003).
3. A Shapere and F Wilczek, “Geometric Phase in Physics”, World Scientific, Singapore (1989).
4. D Xiao, M C Chang, and Q Niu, Rev. Mod. Phys. 82 (2010) 1959.
5. Di Xiao, Shi Junren, and Niu Qian, Phys. Rev. Lett. 95 (2005) 137204.
6. S W Doescher and M H Rice, Am. J. Phys. 37 (1969) 1246.