Negative spectrum in Harmonic oscillator under simultaneous Non-hermitian transformation of co-ordinate and momentum with Real wave function

TL;DR

This paper explores how a PT symmetric non-Hermitian harmonic oscillator, under specific transformations, can exhibit a negative spectrum with real wave functions, supported by computational implementation.

Contribution

It demonstrates the emergence of negative spectra in a PT symmetric non-Hermitian harmonic oscillator through simultaneous coordinate and momentum transformations, with a computational approach.

Findings

Negative spectrum observed under specific transformations.

Real wave functions maintained in real space.

Computational method for negative spectrum realization.

Abstract

We notice that PT symmetric non-Hermitian one dimensional simple Harmonic Oscillator under simultaneous transformation of co-ordinate and momentum with proper choice of positive oscillating frequency can reflect negative spectrum with well behaved wave function in real space. We also present a suitable comuter programme to realise the negative spectrum directly. PACS(2008) : 03.65.Db