The Berry Phase for Simple Harmonic Oscillators

2011/12/12 by Sergeĭ K. Suslov, Suslov, Sergei K.
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1112.2418

openalex publication_date 2011/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Appearance of Gauge Structure in Simple Dynamical Systems
• Particle creation by black holes
• Quantal phase factors accompanying adiabatic changes
• Dynamical Invariants and Berry's Phase for Generalized Driven Harmonic Oscillators

Related

• Berry phase in the simple harmonic oscillator
• Dynamical Invariants and Berry's Phase for Generalized Driven Harmonic Oscillators
• On a Hidden Symmetry of Quantum Harmonic Oscillators
• Relation between the Berry phase in quantum hermitian and non-hermitian systems and the Hannay phase in the equivalent classical systems
• Some geometric features of Berry's phase