- #1
davon806
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Homework Statement
I am not sure about (c) and (d). Firstly, I calculated the eigenvector of A :
|v_1> = ( |2 > - |1> )/ √(2) ,eigenvalue -2
|v_2> = ( |2> + |1>) / √(2) , eigenvalue 2
For (c), basically it follows from part (b) where the probability of a_1 is given by the formula | <v_1 | ψ > |^2 , and similarly for a_2 ( using v_2)
However, I don't see any reason that an extra factor of i will change the value of those probabilities ? ( I've calculated a_1 and a_2 which are both 1/2, in (b) )
For(d), I would like to use the formula ψ(t) = e^(-iEt/h) ψ(0). However, the eigenstates of the Hamiltonian was not provided. Given the fact that we only have |1> , |2> , |v_1> and |v_2> : How can I use this formula?
Homework Equations
In the general case, the Hamiltonian of the system can be written as a 2 × 2 matrix, where the elements of the matrix are given by: H_ij = < i | H | j > . So for example, <2 | A | 1 > = A_21 = 2. Actually A is not the Hamiltonian so I am not even sure whether it is applicable to part (a). Nevertheless I use this in (a). If I was wrong please correct me !
The Attempt at a Solution
Incorporated in question
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