Quantum Mechanics Spin Expectation Value

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Homework Statement


What is the expectation valueof the Sχ for a system in the time-dependent state
|Ψ> = 2e-2iωt |z+> -ieiωt |z->




Homework Equations


maybe the state must be normalised first i.e 1/√5 times the initial ψ


The Attempt at a Solution


And then say<ψ|Sχ|ψ> where ψ is normalised now and Sx is equal to what ?? .
Maybe Sx =hbar/2 ψ ??? i think in this very last statement i have to be wrong
 

Answers and Replies

  • #2
dextercioby
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Who's z+ and z- ? The normalization factor is ok, provided that z+ and z- are normalized.
 
  • #3
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We dont know anything more about z 's ,so this part of problem is solved presumably ,most possibly correct.
 
  • #4
vela
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What do you know about the operator Sx?
 
  • #5
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Maybe it can take half integer values ? I really dont know anything else.
 
  • #6
vela
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Presumably you have a textbook, and it surely covers spin-1/2 systems. Start by reading up on that. Try keeping straight the difference between the operator, its eigenvalues, and its eigenstates. You should be able to calculate what the following equal:
\begin{align*}
\hat{S}_x | \uparrow \rangle = \ ? \\
\hat{S}_x | \downarrow \rangle = \ ?
\end{align*}where the two states are the eigenstates of Sz.
 
  • #7
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the only information i managed to found is that Sx |z+> =hbar/2 |z->

and Sx|z->=hbar/2|z+>

but even if we suppose this is correct there is also the problem how to put these in the expression for the expectation value.
 
  • #8
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well if this is correct i think i know
 
  • #9
vela
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That's correct.
 
  • #10
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3q .
 

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