The Berry Phase for Simple Harmonic Oscillators

Abstract

We evaluate the Berry phase for a "missing" family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables (in a natural way). Instead, it is obtained by the action of the maximal kinematical invariance group on the standard solutions. A simple closed formula for the phase (in terms of elementary functions) is found by integration with the help of a computer algebra system.

7 pages, one figure

References in corpus (3)

• Dynamical Casimir effect in a Josephson metamaterial
• Representations of the Schrödinger group and matrix orthogonal polynomials
• Dynamical Invariants and Berry's Phase for Generalized Driven Harmonic Oscillators

Cited by in corpus (2)

• The Minimum-Uncertainty Squeezed States for for Atoms and Photons in a Cavity
• On a Hidden Symmetry of Quantum Harmonic Oscillators