Meromorphic Behavior of Time Dependent Schroedinger Equation

TL;DR

This paper investigates the meromorphic solutions of the time-dependent Schrödinger equation, revealing that classical particle trajectories exhibit meromorphic behavior within a punctured complex domain, with solutions derived from elliptic functions.

Contribution

It introduces a novel approach to solving the Schrödinger equation using meromorphic functions and pole expansions, linking quantum behavior with complex analysis.

Findings

Particle trajectories are meromorphic in complex domain

Solutions constructed from Jacobi elliptic functions

Branch points lead to solution branching behavior

Abstract

We try to obtain meromorphic solution of Time dependent Schroedinger equation which partially satisfies Painleve Integrable property. Our study and analysis exhibits meromorphic behavior of classical particle trajectory. In other words, particle is confined in punctured complex domain in singular fundamental domain. . We have explicitly developed solution from Jacobi Elliptic function and pole expansion approach in which solution remains meromorphic . Branch point analysis also shows solution branches out near such singular point. Meromorphic behavior is significant for a classical particle within quantum limit.