A Non-Trivial PT-Symmetric Continuum Hamiltonian and Its Eigenstates and Eigenvalues

Authors

Lawrence R. Mead, University of Southern MississippiFollow
Sungwook Lee, University of Southern MississippiFollow
David Garfinkle, Oakland University RochesterFollow

Document Type

Article

Publication Date

7-12-2022

Department

Physics and Astronomy

School

Mathematics and Natural Sciences

Abstract

In this paper, a non-trivial system governed by a continuum PT-symmetric Hamiltonian is discussed. We show that this Hamiltonian is iso-spectral to the simple harmonic oscillator. We find its eigenfunctions and the path in the complex plane along which these functions form an orthonormal set. We also find the hidden symmetry operator, 𝒞, for this system. All calculations are performed analytically and without approximation.

Publication Title

Journal of Mathematical Physics

Volume

63

Issue

7

Recommended Citation

Mead, L. R., Lee, S., Garfinkle, D. (2022). A Non-Trivial PT-Symmetric Continuum Hamiltonian and Its Eigenstates and Eigenvalues. Journal of Mathematical Physics, 63(7).
Available at: https://aquila.usm.edu/fac_pubs/20054