Quantum and classical probability distributions for arbitrary Hamiltonian

TL;DR

This paper compares classical and quantum probability distributions for arbitrary Hamiltonians, extending the analysis to non-standard kinetic terms and validating the approach with a relativistic Hamiltonian.

Contribution

It introduces a generalized method for comparing classical and quantum distributions for complex Hamiltonians, including relativistic cases.

Findings

The approach works for Hamiltonians with non-standard kinetic energy.

Validation with a relativistic Hamiltonian confirms the method's applicability.

Classical-quantum distribution comparison is feasible beyond standard cases.

Abstract

In the limit of large quantum excitations, the classical and quantum probability distributions for a Schr\"odinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is extended for one-dimensional Hamiltonians with a non-usual kinetic part. The validity of the approach is tested with a Hamiltonian containing a relativistic kinetic energy operator.