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HW Phys5405 f01 due Oct. 18,2001
1) Show that the Schrodinger Equation,

¯
h
2
2
m
∇
2
Ψ =
i
¯
h
∂
Ψ
∂t
, is invariant under the Galillean
transform, provided the wave function in the O’ frame is renormalized by a phase, Ψ
0
= Ψ
e
iα
,
where
α
=

mv
¯
h
(
z

vt/
2) and
z
is the direction of relative motion between O and O’. That
is, show that

¯
h
2
2
m
∇
0
2
Ψ
0
=
i
¯
h
∂
Ψ
0
∂t
0
.
2) JDJ 114 (hint  use length contraction)
3) Use the results from the derivation of the Doppler shift, as done in class, to show that the
phase of a wave, 2
π
(
n
·
r
/λ

ft
) is an invariant. Recall the proof was for photons traveling
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This note was uploaded on 12/24/2011 for the course PHYS 5406 taught by Professor Blecher during the Spring '10 term at Virginia Tech.
 Spring '10
 Blecher
 Magnetism, Schrodinger Equation

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