Supersymmetrical separation of variables for Scarf II model: Partial solvability
Saint-Petersburg State University - 198504 St.-Petersburg, Russia
2 Akaki Tsereteli State University - 4600 Kutaisi, Republic of Georgia
Accepted: 12 March 2012
Recently, a new quantum model —two-dimensional generalization of the Scarf II— was completely solved analytically by the SUSY method for the integer values of a parameter. Now, the same integrable model, but with arbitrary values of a parameter, will be studied by means of supersymmetrical intertwining relations. The Hamiltonian does not allow the conventional separation of variables, but the supercharge operator does, leading to the partial solvability of the model. This approach, which can be called the first variant of SUSY separation, together with the shape invariance of the model, provides the analytical calculation of part of the spectrum and corresponding wave functions (quasi-exact solvability). The model is shown to obey two different variants of shape invariance which can be combined effectively in the construction of energy levels and wave functions.
PACS: 03.65.-w – Quantum mechanics / 03.65.Fd – Algebraic methods / 11.30.Pb – Supersymmetry
© EPLA, 2012