Abstract
Using the properties of the generating function of the Hermite polynomials, we have calculated the matrix elements for the Gaussian-type potential
V
G
(x)=A
exp{−B(x−C)
2}
and for the Morse-type potential
V
M(
x)=
D
e[1−exp(−
ax)]
2 in the basis of the non-degenerate harmonic oscillator wavefunctions. The final forms of these matrix elements are very simple to use and hence suitable for the numerical resolution of the Schrödinger equation for multiple-well potentials or anharmonic oscillators.