Bound states in the continuum generated by supersymmetric quantum mechanics and phase rigidity of the corresponding wavefunctions

• Published in: Physics letters. A Vol. 379; no. 42; pp. 2707 - 2714
• Main Authors: Demić, Aleksandar, Milanović, Vitomir, Radovanović, Jelena
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 30.10.2015
• Subjects: Bound states in continuum; Phase rigidity; Supersymmetric quantum mechanics; Bound states in continuum; Supersymmetric quantum mechanics; Phase rigidity
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2015.08.017

Supersymmetric quantum mechanics (SUSYQM) is a method that can be used for generating complex potentials with entirely real spectrum with bound states in the continuum (BIC). These complex potentials are isospectral with the initial one, but SUSYQM method adds discrete BIC's at selected energies. Corresponding wavefunctions created by SUSYQM are biorthogonal and complex, hence we can discuss their phase rigidity and illustrate the application of SUSYQM on the examples of three specific potential profiles (free electron, negative Dirac potential and quantum well with infinite walls). •We present SUSYQM method for generating complex potentials with entirely real spectrum.•Phase rigidity and normalizability of wavefunctions in complex potential is discussed.•Numerical application is performed on three specific potential profiles.