FIZIKA B 3 (1994) 3, 147-166

PHASE-INTEGRAL APPROACH TO ROSEN-MORSE POTENTIALS

NILS DALARSSON
Institute of Theoretical Physics, Uppsala University, Sweden

Received 3 October 1994
Revised manuscript received 25 October 1994

We apply the phase-integral condition to the motion of a quantal particle in the Rosen-Morse potential V(x)=B₀tanh(x/x₀)-U₀cosh^-2(x/x₀) to show that it yields the energy eigenvalues exactly in any order of approximation, when the base function is chosen conveniently. Thereafter, we show that the phase-integral formula for the normalization factors of bound states agrees very satisfactorily with the exact calculation. Finally, we apply the phase-integral formula for the reflexion coefficient to the transmission of a quantal particle through the above potential to show that it gives very accurate results.

UDC 530.145
PACS 03.65.Ge

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