Exact WKB-like Formulae for the Energies by means of the Quantum Hamilton-Jacobi Equation

TL;DR

This paper develops exact WKB-like formulas for quantum energy levels using the Quantum Hamilton-Jacobi approach, improving upon approximate methods and extending previous results on wave functions.

Contribution

It introduces a modified WKB formula for energy levels derived from the Quantum Hamilton-Jacobi equation, providing exact results where traditional WKB is approximate.

Findings

Derivation of exact WKB-like energy formulas

Extension of QHJ method to energy level calculations

Improved accuracy over traditional WKB approximations

Abstract

It is shown that by means of the approach based on the Quantum Hamilton-Jacobi equation, it is possible to modify the WKB expressions for the energy levels of quantum systems, when incorrect, obtaining exact WKB-like formulae. This extends the results found in previous papers, where it was demonstrated that the QHJ method provides exact WKB-like expressions for the wave functions.