A simplified approach to the improved semiclassical method

TL;DR

This paper introduces a simplified method to efficiently compute higher-order terms in the semiclassical quantization condition, making the process more practical while maintaining accuracy for many potentials.

Contribution

It presents a novel approach to obtain next terms in the semiclassical expansion without extra calculations, improving the method's efficiency and applicability.

Findings

Exact results for a wide class of potentials.

Simplifies the calculation of higher-order terms.

Reduces computational effort in semiclassical quantization.

Abstract

The exact semiclassical quantization condition represents a cumbersome series expansion, so that only the main term of it is usually taken into account. We propose a way to find next terms without new additional calculations. Results are exact for a wide class of actual potentials.