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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:
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 the condition required is where changes the parity and transforms to .
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