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Finding spin state.

  • Thread starter cragar
  • Start date
  • #1
2,544
2

Homework Statement


[itex] |\psi >=a|z>+b|-z> [/itex]
find [itex] <S_x > [/itex]

The Attempt at a Solution




So I just need to find
[itex] <S_x>=({|<x|\psi >|}^2-{|<-x|\psi>|}^2)\frac{\hbar}{2} [/itex]
right
 

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
12,490
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Homework Statement


[itex] |\psi >=a|z>+b|-z> [/itex]
find [itex] <S_x > [/itex]

The Attempt at a Solution




So I just need to find
[itex] <S_x>=({|<x|\psi >|}^2-{|<-x|\psi>|}^2)\frac{\hbar}{2} [/itex]
right
Yes, that will get you the answer. If you know the matrix representations of [itex] S_x [/itex], [itex] |z> [/itex], and [itex] |-z> [/itex], then you can also just calculate directly [itex] <S_x>=<\psi |S_x|\psi > [/itex].
 
  • #3
41
0
An easy way to do this problem is to write Sx in terms of the raising and lowering operators. The expectation values of both the raising and lowering operators should be obvious.
 
  • #4
2,544
2
ok thanks for the posts.
If I know what |+x> is. Can I construct |-x> by creating coefficients so that the probability of measuring spin up in the +x and -x equals 1.
 

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