PT symmetry and supersymmetry
Miloslav Znojil
TL;DR
This paper presents a reformulation of supersymmetric quantum mechanics using PT-symmetric Hamiltonians, illustrating novel supersymmetric partnerships with singular harmonic oscillators.
Contribution
It introduces a non-Hermitian, PT-symmetric version of supersymmetric quantum mechanics with new partnerships involving singular oscillators.
Findings
Demonstrates the use of pseudo-Hermitian Hamiltonians in supersymmetry
Provides examples of supersymmetric partnerships with spiked harmonic oscillators
Reviews the theoretical framework of PT-symmetric quantum mechanics
Abstract
A re-formulated, non-Hermitian version of the Witten's supersymmetric quantum mechanics is presented. Its use of pseudo-Hermitian (so called PT symmetric) Hamiltonians is reviewed and illustrated via several forms of an innovated supersymmetric partnership between strongly singular ("spiked") harmonic oscillators.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Noncommutative and Quantum Gravity Theories · Quantum chaos and dynamical systems