Open AccessPT-symmetry and Non-Central Potentials
Author(s) -
G. Lévai
Publication year - 2007
Publication title -
acta polytechnica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.207
H-Index - 15
eISSN - 1805-2363
pISSN - 1210-2709
DOI - 10.14311/932
Subject(s) - eigenfunction , eigenvalues and eigenvectors , polar coordinate system , symmetry (geometry) , separation of variables , transformation (genetics) , norm (philosophy) , physics , polar , mathematics , classical mechanics , mathematical physics , quantum mechanics , geometry , chemistry , boundary value problem , biochemistry , political science , law , gene
We present a general procedure by which solvable non-central potentials can be obtained in 2 and 3 dimensions by the separation of the angular and radial variables. The method is applied to generate solvable non-central PT-symmetric potentials in polar coordinates. General considerations are presented concerning the PT transformation properties of the eigenfunctions, their pseudo-norm and the nature of the energy eigenvalues. It is shown that within the present framework the spontaneous breakdown of PT symmetry can be implemented only in two dimensions.