Abstract
An exactly solvable ring-shaped potential in quantum chemistry given by
was introduced by Hartmann in 1972 to describe ring-shaped molecules like benzene. In this article, the supersymmetric features of the Hartmann potential are discussed, We first review the results of a previous paper in which we rederived the eigenvalues and radial eigenfunctions of the Hartmann potential using a formulation of one-dimensional supersymmetric quantum mechanics (SUSYQM) on the half-line [0, ∞). A reformulation of SUSYQM in the full line (− ∞, ∞) is subsequently developed. It is found that the second formulation makes a connection between states having the same quantum number L but different values of ησ2 and quantum number N. This is in contrast to the first formulation, which relates states with identical values of the quantum number N and ησ2 but different values of the quantum number L.
Similar content being viewed by others
References
Gel'fand YA, Likhtman EP (1971) JETP Lett 13:323
Witten E (1981) Nucl Phys B188:513
For an exhaustive list of references and review of SUSYQM, see Cooper F, Khare A, Sukhatme U (1995) Phys Rep 251:267
Blado GG (1996) Int J Quant Chem 58:431
Hartmann H (1972) Theor Chim Acta 24:201
Hartmann H, Schuch D (1980) Int J Quant Chem 18:125
Haymaker RW, Rau ARP (1986) Am J Phys 54:928
Nilles HP (1984) Phys Rep 110:1
Haber HE, Kane GL (1985) Phys Rep 117:75
Bluhm R, Kostelecky VA (1993) Phys Rev A47:794
See, for example, Griffiths DJ (1995) Introduction to quantum mechanics. Prentice-Hall, Englewood Cliffs, NJ
Schwabl F (1992) Quantum mechanics. Springer, Berlin
Kostelecky VA, Nieto MM (1985) Phys Rev A32:1293
Kostelecky VA, Nieto MM (1984) Phys Rev Lett 53:2285
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Blado, G.G. Supersymmetry and the Hartmann potential of theoretical chemistry. Theoret. Chim. Acta 94, 53–66 (1996). https://doi.org/10.1007/BF00190155
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00190155