Generation of Exactly Solvable Non-Hermitian Potentials with Real Energies

2003/12/10 by Anjana Sinha, Pinaki Roy · 5 citations
Mathematics · Physics and Astronomy · #Eigenvalues and eigenvectors #Excited state #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Series (stratigraphy) #Spectral line #Spectrum (functional analysis) #Transformation (genetics) #quant-ph

paper · pdf · doi:10.1023/b:cjop.0000014377.24971.31

10 pages, 2 figures, Based on the talk presented at the 1st International Workshop "Psedo-Hermitian Hamiltonians in Quantum Physics", held in Prague, June 16, 17, 2003. To be published in Czech. J. Phys. (Jan. 2004)

arxiv created 2003/12/10 · openalex publication_date 2004/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

A series of exactly solvable non-trivial complex potentials (possessing real spectra) are generated by applying the Darboux transformation to the excited eigenstates of a non-Hermitian potential V(x). This method yields an infinite number of non-trivial partner potentials, defined over the whole real line, whose spectra are nearly exactly identical to the original potential.

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