PT -symmetric harmonic oscillators
Abstract
Within the framework of the recently proposed formalism using non-hermitean Hamiltonians constrained merely by their PT invariance we describe a new exactly solvable family of the harmonic-oscillator-like potentials with non-equidistant spectrum. Our one-dimensional superposition of the harmonic x2 with the centrifugal-like G/x2 is regularized by a purely imaginary shift of x.
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