Complex isospectral deformations of conventional shape-invariant superpotentials

Koohrokhi, Taha; Izadpanah, Abdolmajid

doi:10.47176/ijpr.25.2.22029

Complex isospectral deformations of conventional shape-invariant superpotentials

Document Type : Original Article

Authors

Taha Koohrokhi

Abdolmajid Izadpanah

Department of Physics, Faculty of Sciences, Golestan University, Gorgan, Iran

https://doi.org/10.47176/ijpr.25.2.22029

Abstract

All additive shape-invariant superpotentials in nonrelativistic quantum mechanics can be classified into two categories: those that do not explicitly depend on ℏ and those that do. The latter category, known as the conventional superpotentials, forms a complete family. It has been demonstrated that the Schrödinger equation admits exact analytical solutions for this family, highlighting their significance in quantum mechanics due to this and other intriguing properties. This paper presents a mechanism for generalizing these superpotentials to the complex domain. The resulting complex non-Hermitian Hamiltonians possess real energy eigenvalues and are isospectral with their real counterparts.
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Keywords

Superpotential

Complex Superpartners

Non-Hermitian Quantum Mechanics

Parity-Time Reversal Symmetric Quantum Mechanics

Supersymmetric Quantum Mechanics

Subjects

Theoretical

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