Some Theoretical Aspects of Quantum Mechanical Equations in Rindler Space

TL;DR

This paper explores the solutions of quantum mechanical equations in Rindler space, revealing PT symmetry in the Hamiltonian that ensures real energy spectra despite non-Hermiticity.

Contribution

It develops exact and approximate analytical solutions for Schrödinger and Klein-Gordon equations in Rindler space, highlighting the PT symmetry of the Hamiltonian.

Findings

Hamiltonian in Rindler space is non-Hermitian.

Energy eigenvalues are real due to PT symmetry.

Analytical solutions for quantum equations in Rindler space are provided.

Abstract

In this article we have investigated some of the theoretical aspects of the solutions of quantum mechanical equations in Rindler space. We have developed the formalism for exact analytical solutions for Schr$\ddot{\rm{o}}$dinger equation and Klein-Gordon equation. Along with the approximate form of solutions for these two quantum mechanical equations. We have discussed the physical significance of our findings. The Hamiltonian operator in Rindler space is found to be non-Hermitian in nature. But the energy eigen values or the energy eigen spectra are observed to be real. We have noticed that the sole reason behind such real behavior is the PT symmetric form of the Hamiltonian operator.