Eight exactly solvable complex potentials in Bender-Boettcher quantum mechanics

Proceedings of the 20th Winter School "Geometry and Physics", GDML_Books, (2001), p. 213-218 / Harvested from

Résumé

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 $- i$ .

MR MR1826694 | Zbl 0977.81011

EUDML-ID : urn:eudml:doc:221748
Mots clés:

@article{701681,
     title = {Eight exactly solvable complex potentials in Bender-Boettcher quantum mechanics},
     booktitle = {Proceedings of the 20th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2001},
     pages = {213-218},
     mrnumber = {MR1826694},
     zbl = {0977.81011},
     url = {http://dml.mathdoc.fr/item/701681}
}

Znojil, Miloslav. Eight exactly solvable complex potentials in Bender-Boettcher quantum mechanics, dans Proceedings of the 20th Winter School "Geometry and Physics", GDML_Books,  (2001), pp. 213-218. http://gdmltest.u-ga.fr/item/701681/