This preview shows page 1. Sign up to view the full content.
© 2011 E. Szarmes
PHYS 274
DAILY ASSIGNMENT 13 — DUE WEDNESDAY, FEB 16/11
PROF. SZARMES
Q6S.2
According to the superposition principle, the electrons in the recombined beam remain in the

+z
〉
spin
state, but are expressed as a superposition of the

+
ϑ〉
and

–
ϑ〉
states as follows:

+z
〉
=
c
1

+
ϑ〉
+ c
2

–
ϑ〉
=
(
〈
+
ϑ

+z
〉
)

+
ϑ〉
+ (
〈
–
ϑ

+z
〉
)

–
ϑ〉
,
and we wish to check that this is true. First we calculate the coefficients c
1
and c
2
, where
c
1
=
〈
+
ϑ

+z
〉
=
;
c
2
=
〈
–
ϑ

+z
〉
=
Next we substitute the expressions for

+
ϑ〉
and

–
ϑ〉
, and we find that the superposition state is then
which is indeed the

+z
〉
spin state.
Q6S.3
If the electron energy is +E
0
in the

+x
〉
spin state and –E
0
in the

–x
〉
spin state then,
by definition
,
these spin states are also energy eigenstates, since a
definite energy
is associated with each. The first
step is to write the initial state

ψ
(0)
〉
as a superposition of these energy eigenstates:

ψ
(0)
〉
=
=
c
1

+E
0
〉
+ c
2

–E
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 03/07/2011 for the course PHYS 274 taught by Professor Ericszarmes during the Spring '11 term at University of Hawaii, Manoa.
 Spring '11
 EricSzarmes
 Physics

Click to edit the document details