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Teoreticheskaya i Matematicheskaya Fizika, 1971, Volume 6, Number 3, Pages 392–402
(Mi tmf3646)
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This article is cited in 31 scientific papers (total in 31 papers)
Green's functions of the Schrödinger equation for the simplest systems
V. L. Bakhrakh, S. I. Vetchinkin
Abstract:
Closed analytic representations of the Green's functions of the Schrödinger equation are considered
for an harmonic oscillator (linear and three-dimensional isotropie oscillator), the
Morse oscillator, the generalized Kepler problem (the Kratzer potential), and for the double
symmetric potential well $V(x)=\frac{m\omega^2}{2}(|x|-R)^2$. The coordinate representation of the
Green's function is expressed in a form convenient for applications. These models, like
those of free motion and the hydrogen atom (for which closed expressions for the Green's
functions are known), belong to the class of problems for which the Schrödinger equation can
be reduced to the canonical form of the confluent hypergeometric equation.
Received: 26.05.1970
Citation:
V. L. Bakhrakh, S. I. Vetchinkin, “Green's functions of the Schrödinger equation for the simplest systems”, TMF, 6:3 (1971), 392–402; Theoret. and Math. Phys., 6:3 (1971), 283–290
Linking options:
https://www.mathnet.ru/eng/tmf3646 https://www.mathnet.ru/eng/tmf/v6/i3/p392
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