Summing the spectral representations of Poeschl--Teller and Rosen--Morse fixed-energy amplitudes

Journal Article · Sat Feb 01 04:00:00 EST 1992 · Journal of Mathematical Physics (New York); (United States)

DOI:https://doi.org/10.1063/1.529800· OSTI ID:5399539

Kleinert, H; Mustapic, I ^[1]

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1. Institut fuer Theoretische Physik, Freie Universitaet Berlin, Arnimallee 14, D-1000 Berlin 33 (Germany)

The spectral representations of the fixed-energy amplitude of the symmetric and the general Poeschl--Teller potentials are summed via a Sommerfeld--Watson transformation which leads to a simple closed-form expression. The result is used to write down a similar expression for the symmetric and general Rosen--Morse potentials, exploiting the close correspondence that exists between the two systems within the Schroedinger theory and the path integral formalism via a Duru--Kleinert transformation. From the singularities of the latter amplitude the bound and continuum states of the general Rosen--Morse potential are extracted.

• OSTI ID: 5399539
• Journal Information: Journal of Mathematical Physics (New York); (United States), Journal Name: Journal of Mathematical Physics (New York); (United States) Vol. 33:2; ISSN JMAPA; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLITUDES
BOUND STATE
DIFFERENTIAL EQUATIONS
EIGENVALUES
ENERGY LEVELS
EQUATIONS
FEYNMAN PATH INTEGRAL
FUNCTIONS
INTEGRALS
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
SCHROEDINGER EQUATION
SINGULARITY
SOMMERFELD-WATSON THEORY
WAVE EQUATIONS
WAVE FUNCTIONS