New types of solvability in PT symmetric quantum theory Miloslav Znojil
(znojil@ujf.cas.cz)
Abstract The remarkable increase of popularity of the models with real spectra generated by non-Hermitian Hamiltonians will be reviewed. The new type of their characteristic (so called PT) symmetry will be presented as a source of new forms of integrability and solvability based on (a) a new approach to the (suitably complexified) boundary conditions, (b) the related modification of the concepts of creation operators and supersymmetry, (c) the occurrence of an alternative metric in Hilbert space, (d) an emergence of certain implicit analyticity assumptions leading to various natural regularization recipes. Some specific consequences of these properties for superintegrable systems will be analyzed in more detail. |