Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

$\mathcal{PT}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions (1301.0205v1)

Published 2 Jan 2013 in math-ph, math.MP, and quant-ph

Abstract: In this article, we have introduced a $\mathcal{PT}$ symmetric non-Hermitian Hamiltonian model which is given as $\hat{\mathcal{H}}=\omega (\hat{b}{\dag}\hat{b}+1/2)+ \alpha (\hat{b}{2}-(\hat{b}{\dag}){2})$ where $\omega$ and $\alpha$ are real constants, $\hat{b}$ and $\hat{b{\dag}}$ are first order differential operators. The Hermitian form of the Hamiltonian $\mathcal{\hat{H}}$ is obtained by suitable mappings and it is interrelated to the time independent one dimensional Dirac equation in the presence of position dependent mass. Then, Dirac equation is reduced to a Schr\"{o}dinger-like equation and two new complex non-$\mathcal{PT}$ symmetric vector potentials are generated. We have obtained real spectrum for these new complex vector potentials using shape invariance method. We have searched the real energy values using numerical methods for the specific values of the parameters.

Summary

We haven't generated a summary for this paper yet.