Eight exactly solvable complex potentials in Bender-Boettcher quantum mechanics

Znojil, Miloslav

  • Proceedings of the 20th Winter School "Geometry and Physics", Publisher: Circolo Matematico di Palermo(Palermo), page 213-218

Abstract

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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 ) = ω 2 2 x - 2 i β ω 2 - 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 .

How to cite

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Znojil, Miloslav. "Eight exactly solvable complex potentials in Bender-Boettcher quantum mechanics." Proceedings of the 20th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2001. 213-218. <http://eudml.org/doc/221748>.

@inProceedings{Znojil2001,
abstract = {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: \[ V(x)=\frac\{\omega ^2\}\{2\}\,\left(x-\frac\{2i\beta \}\{\omega \}\right)^2-\frac\{\omega \}\{2\}.\] 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 $H=PTHPT$ where $P$ changes the parity and $T$ transforms $i$ to $-i$.},
author = {Znojil, Miloslav},
booktitle = {Proceedings of the 20th Winter School "Geometry and Physics"},
keywords = {Winter school; Proceedings; Geometry; Physics; Srní(Czech Republic)},
location = {Palermo},
pages = {213-218},
publisher = {Circolo Matematico di Palermo},
title = {Eight exactly solvable complex potentials in Bender-Boettcher quantum mechanics},
url = {http://eudml.org/doc/221748},
year = {2001},
}

TY - CLSWK
AU - Znojil, Miloslav
TI - Eight exactly solvable complex potentials in Bender-Boettcher quantum mechanics
T2 - Proceedings of the 20th Winter School "Geometry and Physics"
PY - 2001
CY - Palermo
PB - Circolo Matematico di Palermo
SP - 213
EP - 218
AB - 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: \[ V(x)=\frac{\omega ^2}{2}\,\left(x-\frac{2i\beta }{\omega }\right)^2-\frac{\omega }{2}.\] 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 $H=PTHPT$ where $P$ changes the parity and $T$ transforms $i$ to $-i$.
KW - Winter school; Proceedings; Geometry; Physics; Srní(Czech Republic)
UR - http://eudml.org/doc/221748
ER -

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