A Geometric Picture of the Wave Function: Fermi's Trick

TL;DR

This paper presents a geometric interpretation of the wave function by establishing a one-to-one correspondence with phase space surfaces satisfying a refined quantum condition, utilizing Fermi's idea.

Contribution

It introduces a novel geometric framework linking wave functions to phase space surfaces with an exact quantum condition, refining traditional EBK quantization.

Findings

Establishes a one-to-one correspondence between wave functions and phase space surfaces.

Refines the EBK quantization condition using Fermi's approach.

Provides a geometric perspective on quantum states.

Abstract

We show that there is a one-to-one correspondence between wave functions and surfaces in the position-momentum phase plane bounded by a closed curve satisfying an exact quantum condition refining the usual EBK condition. This is achieved using an old forgotten idea of Enrico Fermi.