A generalized potential in the theory of the Rabi and Jahn-Teller systems. II

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The eigenvalue problem for the Rabi and Jahn-Teller Hamiltonians in Bargmann's Hilbert space is a system of two first-order differential equations for the two-component wavefunctions for which entire solutions are sought. The concept of the generalized potential has been introduced in a previous paper together with a particular example. Here we treat a simpler potential N(z) which satisfies a second-order ordinary differential equation closely related to the differential equation of the confluent Heun functions. The component wavefunctions are linear in the potential and its first derivative. The coefficients of N(z) and dN(z)/dz are functions of z and the physical parameters which are identical in all eigenstates. The relation to the previous example is fully discussed.
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Fakultät / Institut:
Fakultät für Mathematik
Dewey Dezimal-Klassifikation:
500 Naturwissenschaften und Mathematik » 510 Mathematik » 515 Analysis
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In: Journal of physics. A. Mathematical and General, 27 (1994) S. 6907-6918