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Physics Letters A

Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex -invariant potential

Zafar Ahmed

Published Apr 1, 2001• 362 citations
Publisher
DOI
10.1016/s0375-9601(01)00218-3

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The spectrum of a one-dimensional Hamiltonian with potential V(x)=ix2V(x)=ix^2V(x)=ix2 for negative xxx and V(x)=−ix2V(x)=-ix^2V(x)=−ix2 for positive xxx is analyzed. The Schrödinger equation is algebraically solvable and the eigenvalues are obtained as the zeros of an expression explicitly given in terms of Gamma functions. The spectrum consists of one real eigenvalue and an infinite set of pairs of complex conjugate eigenvalues.