Annihilation and creation operators in non-Hermitian supersymmetric quantum mechanics

2000/12/01 by Miloslav Znojil, Znojil, Miloslav · 2 citations
Physics and Astronomy · #Advanced Fiber Laser Technologies #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/0012002

19 pages and 7 tables for Tuesday seminar in Bratislava. Version 2: 15 pages, submitted

openalex publication_date 2000/12/01 · arxiv created 2001/04/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Harmonic oscillators with a centrifugal spike are analysed, via a non-Hermitian regularization, within a complexified SUSY quantum mechanics. The formalism enables us to construct the factorized creation and annihilation operators. We show how the real though, generically, non-equidistant spectrum complies with the current SUSY-type isospectrality and degeneracy in an unusual way.

Cited by

• Non-Hermitian supersymmetry and singular, 𝒫𝒯-symmetrized oscillators
• Pseudo supersymmetric partners for the generalized Swanson model

Related

• Equivalent non-rational extensions of the harmonic oscillator, their ladder operators and coherent states
• Supersymmetric Quantum Mechanics: two factorization schemes, and quasi-exactly solvable potentials
• Non-Hermitian N-state degeneracies: unitary realizations via antisymmetric anharmonicities
• A Study about the Supersymmetry in the context of Quantum Mechanics
• New Supercoherent States