We show that the connection between Wick ordered polynomials and Hermite polynomials derived by Wurm and Berg by an inductive method can be directly and concisely obtained using the technique of integration within an ordered product of operators (IWOP).

1.
Alexander
Wurm
and
Marcus
Berg
, “
Wick calculus
,”
Am. J. Phys.
76
,
65
72
(
2008
).
2.
G. C.
Wick
, “
The evaluation of the collision matrix
,”
Phys. Rev.
80
,
268
272
(
1950
).
3.
Hong-yi
Fan
,
Hai-Liang
Lu
, and
Yue
Fan
, “
Newton-Leibniz integration for ket-bra opertors in quantum mechanics and derivation of entangled state representations
,”
Ann. Phys.
321
,
480
494
(
2006
).
4.
Hong-yi
Fan
, “
Operator ordering in quantum optics theory and thedevelopment of Dirac’s symbolic method
,”
J. Opt. B: Quantum Semiclassical Opt.
5
,
R147
R163
(
2003
).
5.
Alfred
Wünsche
, “
About integration within ordered products in quantum optics
,”
J. Opt. B: Quantum Semiclassical Opt.
1
,
R11
R21
(
1999
).
6.
D. F.
Walls
and
G. J.
Milburn
,
Quantum Optics
(
Springer-Verlag
,
Berlin
,
1994
).
7.
I. S.
Gradshteyn
and
L. M.
Ryzhik
,
Table of Integrals, Series and Products
(
Academic Press
,
New York
,
1980
), p.
837
.
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