Conditionally exactly solvable potential and dual transformation in quantum mechanics

Abstract

We comment that the conditionally exactly solvable potential of Dutt et al (1995 J. Phys. A: Math. Gen. 28 L107) and the exactly solvable potential from which it is derived form a dual system.

Rationally extended many-body truncated Calogero–Sutherland model

“…Beyond being of academic interest, both QES and CES potentials provide valuable insights in the characterization of physical phenomena. In particular, a connection between QES and spin-boson and spin-spin interacting systems is well known [38], and the dual partnership between CES and the accompanying shape invariant ES potential was pointed out some time ago [39].…”

Novel exactly solvable Schrödinger equations with a position-dependent mass in multidimensional spaces obtained from duality

“…A clue to this construction is the relationship between the d-dimensional harmonic oscillator problem and the D-dimensional Coulomb one in Euclidean spaces for specific values of the pair (d, D), resulting from coupling-constant metamorphosis [11], Stäckel transform [12], regularization of the Coulomb problem [13,14,15], supersymmetry [16], or duality tranformation [17]. Since the latter is a very simple and powerful method for generating new exactly solvable potentials (see, e.g., [18]), we choose to apply it in the present case. We plan to extend it to curved spaces, then to reinterprete the relation so obtained in a PDM background.…”