Using the algebraic second quantization formalism, the general recurrence relations for some two‐center harmonic oscillator integrals are obtained. The various known special cases for one‐center integrals are evident in the formalism. Generating functions for these integrals are obtained and most of them are solved to find explicit expressions for polynomial, exponential, and Gaussian operator integrals. For these cases, all the generating integrals needed for utilizing the recurrence relations are also calculated in their simplest forms.

1.
J.
Morales
,
L.
Sandoval
, and
A.
Palma
,
J. Math. Phys.
27
,
2966
(
1986
).
Google Scholar
Crossref
Search ADS
 
2.
J.
Morales
,
A.
Palma
, and
M.
Berrondo
,
Int. J. Chem.
S18
,
57
(
1985
).
Google Scholar
 
3.
J.
Morales
,
J.
Zopez‐Bonilla
, and
A.
Palma
,
J. Math. Phys.
28
,
1032
(
1987
).
Google Scholar
Crossref
Search ADS
 
4.
Note that the definition of Laguerre polynomials is not standardized. We are using the one in Ref. 5.
5.
I. M. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1965).
6.
See Eq. (2.15) in Ref. 3.
7.
See Eq. (8.335(1)) in Ref. 5.
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© 1989 American Institute of Physics.
1989
American Institute of Physics
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