An algebraically solvable PT-symmetric potential with broken symmetry

E. M. Ferreira; J. Sesma

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arXiv · 1401.5937

An algebraically solvable PT-symmetric potential with broken symmetry

E. M. Ferreira·J. Sesma

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Abstract

The spectrum of a one-dimensional Hamiltonian with potential $V(x)=ix^2$ for negative $x$ and $V(x)=-ix^2$ for positive $x$ 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.

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E. M. Ferreira, J. Sesma. 2014-01-23. An algebraically solvable PT-symmetric potential with broken symmetry. https://arxiv.org/abs/1401.5937

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