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The complete solution of the Schrödinger equation with the Rosen-Morse type potential via the Nikiforov-Uvarov method. (English) Zbl 07808491

Summary: We determine exact solutions of the time-independent Schrödinger equation for the Rosen-Morse type potential by using the Nikiforov-Uvarov method. This method allows us to write the eigenfunctions of the Schrödinger equation as the product of two simpler functions in a constructive way. The resolution of this problem is used to show that the kinks of the non-linear Klein-Gordon equation with \(\varphi^{2p + 2}\) type potentials are stable. We also derive the orthogonality and completeness relations satisfied by the set of eigenfunctions, which are useful in the description of the dynamics of kinks under perturbations or interacting with antikinks.

MSC:

37Kxx Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems
33Cxx Hypergeometric functions
81Qxx General mathematical topics and methods in quantum theory

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