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Real exact solutions to the relativistic spinless particle with modified Rosen–Morse potential and its 𝒫𝒯 symmetry
Author(s) -
Qiang W.C.,
Sun G.H.,
Dong S.H.
Publication year - 2012
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.201200030
Subject(s) - physics , eigenfunction , morse potential , eigenvalues and eigenvectors , hermitian matrix , symmetry (geometry) , mathematical physics , dirac equation , dirac (video compression format) , quantum mechanics , mathematics , geometry , neutrino
The real exact solutions to the relativistic spinless particle with modified Rosen–Morse potential are presented. The novel issue is that the previously obtained eigenfunctions related to this type of potential in an imaginary variable i sinh (α x) (Dirac case) can be expressed by the real Nomanovski polynomials. The energy levels are calculated numerically. It is interesting to note that the energy levels first increase with the parameter V 1 (V 1 <0) and then decrease with it. In the case of the symmetric version it is found that the eigenvalues are real even though the symmetric potentials are non‐Hermitian.