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)=mω22(|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.
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
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