Classical equivalents for quantum eigenfunctions in energy representation for simple hamiltonian systems

TL;DR

This paper derives classical analogues of quantum eigenfunctions and local density of states for simple Hamiltonian systems, extending semiclassical methods to both simple and scalable systems with analytical expressions.

Contribution

It introduces explicit classical equivalents for quantum eigenfunctions in energy representation for simple Hamiltonian systems, expanding previous semiclassical approaches.

Findings

Analytical expressions for classical analogues are obtained for simple systems.

Examples demonstrate the applicability of the derived formulas.

The method extends to scalable systems, broadening its usefulness.

Abstract

A calculation of the classical analogue for the quantum wave function and local denity of states, in energy representation, is presented for simple Hamiltonian systems. Sucha analogous were proposed by M. V. Berry and A. voros considering the intersection of energy shells of two systems as the only semiclassical object which can give support to eigenfunctions. One of them is the system unser study and the other is the "unperturbed system" used to express the wave functions, even in the case that both systems are not close. For simple systems and as for scalable ones analytical expressions are obtainable. In the present work we offer examples of both.