We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed “distorted” Heisenberg algebra (including the q-generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the Hilbert space. Formal representations of the nonlocal operators concerned are given in terms of pseudo-differential operators. Using the new annihilation operators, new classes of coherent states are constructed for isospectral oscillator Hamiltonians. The corresponding Fock–Bargmann representations are also considered, with specific reference to the order of the entire function family in each case.

1.
C. M.
Caves
and
B. L.
Schumaker
,
Phys. Rev. A
31
,
3068
,
3093
(
1985
).
2.
H. P.
Yuen
,
Phys. Rev. A
13
,
2226
(
1976
).
3.
G. S.
Agarwal
,
J. Opt. Soc. Am. B
5
,
1940
(
1988
).
4.
C. L.
Mehta
,
A. K.
Roy
, and
G. M.
Saxena
,
Phys. Rev. A
46
,
1565
(
1992
).
5.
P.
Shanta
,
S.
Chaturvedi
,
V.
Srinivasan
,
G. S.
Agarwal
, and
C. L.
Mehta
,
Phys. Rev. Lett.
72
,
1447
(
1994
).
6.
S.
Seshadri
,
S.
Lakshmibala
, and
V.
Balakrishnan
,
Phys. Rev. A
55
,
869
(
1997
).
7.
D. J.
Fernandez
,
V.
Hussin
, and
L. M.
Nieto
,
J. Phys. A
27
,
3547
(
1994
).
8.
M. S.
Kumar
and
A.
Khare
,
Phys. Lett. A
217
,
73
(
1996
).
9.
A. Perelomov, Generalized Coherent States and Their Applications (Springer-Verlag, Berlin, 1986).
10.
D. J.
Fernandez
,
L. M.
Nieto
, and
O.
Rosas-Ortiz
,
J. Phys. A
28
,
2693
(
1995
);
O.
Rosas-Ortiz
,
J. Phys. A
29
,
3281
(
1996
).
11.
M. Simon and B. Reed, Methods of Modern Mathematical Physics (Academic, New York, 1972), Vol. I.
12.
I. M.
Gel’fand
and
L. A.
Dikii
, Funkts. Anal. Prilozhen. 10, 13 (1976) [
Funct. Anal. Appl.
10
,
259
(
1976
)].
13.
S.
Chaturvedi
and
V.
Srinivasan
,
Phys. Rev. A
44
,
8020
(
1991
).
14.
I. M.
Gel’fand
and
L. A.
Dikii
,
Usp. Mat. Nauk
30
,
67
(
1975
). [Russ. Math. Surv. 30, 77 (1975)].
15.
V. Guillemin and S. Sternberg, Symplectic Techniques in Physics (Cambridge U.P., Cambridge, 1990).
16.
V.
Bargmann
,
Commun. Pure Appl. Math.
14
,
187
(
1961
).
17.
E. C. Titchmarsh, The Theory of Functions (Oxford U.P., London, 1962).
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