PHYS 302
: Unit 15 Quantum Mechanics Supplement –
Athabasca University
1
Unit 15 Resonant Cavities: Quantum Resonance
After completing this Unit 15 supplement, you should be able to
1.
identify that the wave equation can be solved in cylindrical and spherical coordinate systems.
2.
describe boundary conditions suited to cylindrical and spherical coordinate systems.
3.
describe atomic energy levels arising from wave effects in atoms, and determine the energy of
EMradiation arising from transitions between two atomic energy levels.
In French (p. 246, Eq. 744), the wave equation governing a symmetric wave is
2
2
2
2
2
2
1
r
r
r
v
t
. Eq. 745 gives
one solution as
( , )
sin 2
(
)
C
r
r t
vt
kr
. This makes sense, since the energy per unit area of such a wave
would go to zero at infinity (i.e., it would spread out with distance to become imperceptible). Another boundary
condition would have to be supplied to determine
C
; this might be the wave on a surface of known radius.
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 Spring '10
 martinconner
 mechanics, wave equation, Spherical Coordinate Systems, Quantum Mechanics Supplement

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