The Scarf I and Scarf II potentials are discussed within a common mathematical framework, which is then specified to handle the two potentials separately both in the conventional Hermitian and in the PT-symmetric setting. The physically admissible solutions are identified in each case together with the corresponding energy eigenvalues. Several main differences between the PT-symmetric Scarf I and II potentials are pointed out. These include the presence and absence of the quasi-parity quantum number, the sign of the pseudo-norm, the mechanism of the spontaneous breakdown of PT symmetry and the non- PT orthogonality of otherwise admissible solutions in the Scarf I potential. Similarities and differences with respect to the corresponding Hermitian systems are also pointed out.
- PT symmetry
- Singular potentials
- Spontaneous breakdown of PT symmetry
ASJC Scopus subject areas
- Physics and Astronomy(all)