It is demonstrated for one‐dimensional Hamiltonians, and under a special hypothesis on the ground state wave function, that it is possible to build an analytical overcomplete basis that generalizes the coherent state basis of the harmonic oscillator, without any reference to group theory. The semi‐classical consequences of this formalism are developed and the usual ideas of normal and antinormal expansions for operators are extended.

1.
J. R. Klauder, Coherent States, Applications in Physics and Mathematical Physics, edited by J. R. Klauder and B. S. Skagerstam (World Scientific, Singapore, 1985).
2.
A. M.
Perelomov
,
Commun. Math. Phys.
222
(
1972
).
3.
A. M. Perelomov, Generalized Coherent States and Their Applications (Springer, Berlin, 1986).
4.
J. R.
Klauder
,
Phys. Rev. D
19
,
2349
(
1979
).
5.
T.
Fukui
and
N.
Aizawa
,
Phys. Lett. A
180
,
308
(
1993
).
6.
L. E.
Gendenstein
,
JETP Lett.
38
,
356
(
1983
).
7.
B. W.
Fatyga
,
V. A.
Kostelecky
,
M. M.
Nieto
, and
D. R.
Truax
,
Phys. Rev. D
43
,
1403
(
1991
).
8.
M. M.
Nieto
and
L. M.
Simmons
,
Phys. Rev. D
20
,
1321
(
1979
).
9.
E.
Witten
,
Nucl. Phys. B
185
,
513
(
1981
).
10.
C. V.
Sukumar
,
J. Phys. A
18
,
L57
(
1985
).
11.
F.
Cooper
and
B.
Freedman
,
Ann. Phys.
151
,
262
(
1983
).
12.
J.
Fuchs
,
Ann. Phys.
165
,
285
(
1985
).
13.
R.
Dutt
,
A.
Khare
, and
U. P.
Sukhatme
,
Am. J. Phys.
56
,
163
(
1988
).
14.
A.
Valance
and
H.
Bergeron
,
J. Phys. B
22
,
L65
(
1989
).
15.
A.
Valance
and
H.
Bergeron
,
Phys. Lett. A
135
,
276
(
1989
).
16.
A.
Comtet
,
A.
Bandrauk
, and
D.
Campbell
,
Phys. Lett. A
150B
,
159
(
1985
).
17.
A.
Khare
,
Phys. Lett. A
161B
,
131
(
1985
).
18.
R. J.
Glauber
,
Phys. Rev.
131
,
2766
(
1963
).
19.
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Functional Analysis, p. 330.
20.
K. E.
Cahill
and
R. J.
Glauber
,
Phys. Rev.
177
,
1857
(
1969
).
21.
E.
Gozzi
,
Phys. Lett. A
129B
,
432
(
1983
).
22.
A. M.
Perelomov
,
Sov. J. Nucl. Phys.
29
,
867
(
1979
).
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