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Eight exactly solvable complex potentials in Bender-Boettcher quantum mechanics

Znojil, Miloslav — 2001

Proceedings of the 20th Winter School "Geometry and Physics"

This is a readable review of recent work on non-Hermitian bound state problems with complex potentials. A particular example is the generalization of the harmonic oscillator with the potentials: $V (x) = \frac{ω^{2}}{2} {(x - \frac{2 i β}{ω})}^{2} - \frac{ω}{2} .$ Other examples include complex generalizations of the Morse potential, the spiked radial harmonic potential, the Kratzer-Coulomb potential, the Rosen Morse oscillator and others. Instead of demanding Hermiticity $H = H^{*}$ the condition required is $H = P T H P T$ where $P$ changes the parity and $T$ transforms $i$ to $- i$ .

On the role of the normalization factors $κ_{n}$ and of the pseudo-metric $𝒫 \neq 𝒫^{†}$ in crypto-Hermitian quantum models.

Znojil, Miloslav — 2008

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Three-Hilbert-space formulation of quantum mechanics.

Znojil, Miloslav — 2009

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Planarizable supersymmetric quantum toboggans.

Znojil, Miloslav — 2011

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Currently displaying 1 – 8 of 8

Eight exactly solvable complex potentials in Bender-Boettcher quantum mechanics

Multiparametric oscillator Hamiltonians with exact bound states in infinite-dimensional space

Conservation of pseudo-norm in $𝒫 𝒯$ symmetric quantum mechanics

Re-establishing supersymmetry between harmonic oscillators in $D \neq 1$ dimensions

Cryptohermitian picture of scattering using quasilocal metric operators.

On the role of the normalization factors $κ_{n}$ and of the pseudo-metric $𝒫 \neq 𝒫^{†}$ in crypto-Hermitian quantum models.

Three-Hilbert-space formulation of quantum mechanics.

Planarizable supersymmetric quantum toboggans.