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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 ) = 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 .

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