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Probability of Finding System in a State Given a Particular Basis
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[QUOTE="The Head, post: 4303056, member: 321011"] So I am assuming to find a1 I simply perform <δ1|ω1>, and I would get a1=i/sqrt(3), and similarly a2=sqrt(2/3), a3=0, and then I could put |ω1> into column form: (a1) (a2) (a3) (that is my attempt at a column matrix). I could do a similar thing for |ω2> to get coefficients b1=(1+i)/sqrt(3), b2=1/sqrt(6)=b3. To calculate the probability of being in |ω2>, what I am tempted to do is now perform the operation |<ω2|ω1>|^2/<ω1|ω1>, which yields 5/9, if I calculated correctly. But I am not entirely confident in the strategy. I go back and forth with this, but I feel like the ω terms are the eigenvectors representing two different eigenvalues/states. But at the same time, I feel like I am treating ω1 as my initial state vector (like ψ(0)), and then projecting a specific state, ω2 in this case, onto ψ. So, is the strategy seem like it is correct, or did I go fishing? Also, did anything I say in the previous paragraph resemble the reality of the situation? Thank you! [/QUOTE]
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Probability of Finding System in a State Given a Particular Basis
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