A reality proof in PT-symmetric quantum mechanics

Abstract

We review the proof of a conjecture concerning the reality of the spectra of certain PT-symmetric quantum mechanical systems, obtained via a connection between the theories of ordinary differential equations and integrable models. Spectral equivalences inspired by the correspondence are also discussed.

arXiv comment7 pages, 2 figures, latex. Contribution to the proceedings of Pseudo-Hermitian Hamiltonians in Quantum Physics, Prague, 2003

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Cited by in corpus (17)

• Making Sense of Non-Hermitian Hamiltonians
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
• Curving the space by non-Hermiticity
• Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
• Appropriate Inner Product for PT-Symmetric Hamiltonians
• Experiments in PT-symmetric quantum mechanics
• Exact solution of a non-Hermitian $\mathcal{PT}$-symmetric Heisenberg spin chain
• Spiked potentials and quantum toboggans
• Quantum toboggans
• A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length
• PT symmetry in relativistic quantum mechanics
• Metric operators for non-Hermitian quadratic su(2) Hamiltonians
• Lower bound of minimal time evolution in quantum mechanics
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor
• A(2|1) spectral equivalences and nonlocal integrals of motion
• Comment on "Numerical estimates of the spectrum for anharmonic PT symmetric potentials" by Bowen et al