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Plasma Harmonics
book

Plasma Harmonics

by Rashid A. Ganeev
June 2014
Intermediate to advanced content levelIntermediate to advanced
320 pages
9h 1m
English
CRC Press
Content preview from Plasma Harmonics
April 25, 2014 11:1 PSP Book - 9in x 6in 06-Rashid-A.-Ganeev-c06
196 Characterization of Plasma Harmonics
It is convenient to introduce the following transformation matrix
V
nm
(
t
)
=
u
n
(
r
)
exp
i
q
c
χ
(
r, t
)
u
m
(
r
)
dV. (6.8)
As we have mentioned above, in the case
χ
(
r, t
)
= A
(
t
)
r, (6.9)
the Hamiltonian of the problem (6.4) takes the form
H =
1
2m
p
q
c
A
(
t
)
2
+U
(
r
)
.
and coincides with the Hamiltonian of Eq. (6.1). Hence, the
eigenfunctons of the Hamiltonian of the TDSE are
ϕ
n
(
r, t
)
= u
n
(
r
)
exp
i
q
c
A
(
t
)
r
. (6.10)
One can see that Eq. (6.10) looks similar to the formula for
gauge transformation proposed by Goppert–Mayer [58]. However,
it should be noted here that this
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Publisher Resources

ISBN: 9789814463300