# PT-Symmetric Quantum Mechanics: (NxN) Matrix Model

## TL;DR

This paper introduces a complex-conjugate-space model for PT-symmetric quantum mechanics using (NxN) matrices, clarifying symmetry properties and showing consistency with known N=2 cases, advancing understanding of non-Hermitian systems.

## Contribution

It proposes a novel CCS framework for PT-symmetric models and extends symmetry analysis to arbitrary N, aligning with established N=2 results.

## Key findings

- CCS model clarifies wave function inner and outer products in PT-symmetry.
- Symmetry properties are consistent with known N=2 cases.
- Wave functions exhibit relations similar to Hermitian operators.

## Abstract

We propose a model CCS (complex-conjugate-space) to understand the inner and outer product nature of wave functions in non-hermitian PT-symmetry model in quantum mechanics considering (NxN) matrix model. Further we reflect the correct nature of C-symmetry ,P-parity and original Hamiltonian matrix for any arbitrary values of N. Interestingly the present result on N=2 , remains the same reported earlier by Bender,Brody and Jones model PT-symmetry operator. In non-conventional way one can notice that wave functions in a PT-symmetry model satisfies similar relations as in hermitian operator .