Quantum-Classical Correspondence in a Quartic Oscillator -- Corrections to Frequency and Bounds for Periodic Motion

• URL: http://arxiv.org/abs/2410.09722v1
• Date: Sun, 13 Oct 2024 04:30:39 GMT
• Title: Quantum-Classical Correspondence in a Quartic Oscillator -- Corrections to Frequency and Bounds for Periodic Motion
• Authors: Mandas Biswas, Deb Shankar Ray,
• Abstract summary: We take a comparative look at the behavior of quantum and classical quartic anharmonic oscillators. The associated equation of motion allows us to compute the classical frequency of the oscillation order by order. We derive a bound for periodicity of such oscillations in both the classical and quantum cases.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We take a qualitative comparative look at quantum and classical quartic anharmonic oscillators. It has been shown that the behavior of the quantum anharmonic oscillator mimics that of the classical anharmonic oscillators with the structurally same Hamiltonian in the coherent state basis of the harmonic oscillators. The associated equation of motion allows us to use Lindstet-Poincare perturbation method to compute the classical frequency of the oscillation order by order, by taking care of its dependence on amplitude and the quantum corrections. We also derive a bound for periodicity of such oscillations in both the classical and quantum cases.

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