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Quantum Mechanical Motions over the Group Manifolds and Related Potentials

In: Symmetries in Science VIII

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  • I. H. Duru

    (Trakya University, Department of Mathematics
    Marmara Research Center, TUBITAK)

Abstract

Schrödinger equations for many potentials are solved in terms of the special functions. Almost all of these special functions are the matrix elements of the representations of the Lie groups, with their arguments being the group parameters [1,2]. Even the simplest “special functions” namely the elementary transcendentals are related to the Lie groups, i.e., the one parameter Abelian Lie groups. The connection between the group representations and the special functions explains the mystrious properties of them, such as the recurance relations and addition theorems.

Suggested Citation

  • I. H. Duru, 1995. "Quantum Mechanical Motions over the Group Manifolds and Related Potentials," Springer Books, in: Bruno Gruber (ed.), Symmetries in Science VIII, pages 91-100, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-1915-7_9
    DOI: 10.1007/978-1-4615-1915-7_9
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