Time Dependent Rindler Hamiltonian Eigen States in Momentum Space

TL;DR

This paper presents a formalism for analyzing the time evolution of Rindler Hamiltonian eigenstates in momentum space, overcoming computational challenges by reformulating the problem as a 2D Laplace equation and solving it in different coordinate systems.

Contribution

It introduces a novel approach to compute the time evolution of Rindler eigenstates in momentum space by transforming the problem into a 2D Laplace equation.

Findings

Solutions obtained in polar coordinates

Solutions obtained in Cartesian coordinates

Demonstrated the formalism's effectiveness

Abstract

We have developed a formalism to get the time evolution of the eigen states of Rindler Hamiltonian in momentum space. We have shown the difficulties with characteristic curves, and re-cast the time evolution equations in the form of two-dimensional Laplace equation. The solutions are obtain both in polar coordinates as well as in the Cartesian form.