An algebraically solvable PT-symmetric potential with broken symmetry

2014/01/23 by E. M. Ferreira, Ferreira, E. M., J. Sesma +1
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.1401.5937

6 pages

arxiv created 2014/01/23 · arxiv updated 2014/01/24

Abstract

The spectrum of a one-dimensional Hamiltonian with potential V(x)=ix² for negative x and V(x)=-ix² 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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