Considerations about the Aharonov-Anandan Phase for Time Independent Hamiltonians

TL;DR

This paper introduces a new method for calculating the Aharonov-Anandan phase in time-independent Hamiltonians that simplifies the process by avoiding evolution operator calculations, demonstrated through four diverse examples.

Contribution

The paper proposes a novel approach to compute the Aharonov-Anandan phase without using evolution operators, applicable to various quantum systems.

Findings

The new method simplifies phase calculation in quantum systems.

Comparison shows the new method matches traditional results.

Applicable to systems like spin-1/2 particles and optical cavities.

Abstract

We present a method for calculating the Aharonov-Anandan phase for time-independent Hamiltonians that avoids the calculation of evolution operators. We compare the generic method used to calculate the Aharonov-Anandan phase with the method proposed here through four examples; a spin-1/2 particle in a constant magnetic field, an arbitrary infinite-sized Hamiltonian with two known eigenvalues, a Fabry-Perot cavity with one movable mirror and a three mirrors cavity with a slightly transmissive movable middle mirror.