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ma18
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Homework Statement
The e-states of H^0 are
phi_1 = (1, 0, 0) , phi_2 = (0,1,0), phi_3 = (0,0,1) *all columns
with e-values E_1, E_2 and E_3 respectively.
Each are subject to the perturbation
H' = beta (0 1 0
1 0 1
0 1 0)
where beta is a positive constant
a) If E_1 =/ E_2 =/ E_3
What are the new energy levels according to first and second-order perturbation theory
b) If E_1 = E_2 = E_3
What are the new energy levels according to first degenerate perturbation theory
c) If E_1 =/ E_2 = E_3
What are the new energy levels according to first perturbation theory
Homework Equations
For first order non degenerate perturbation:
E_n ^1 = <phi_n ^ 0 | H' | phi_n ^ 0>
For second order perturbation
E_n ^2 = Σ (m=/n) of (|phi_m ^0 | H' | phi_n ^ 0>|^2)/(E_n ^ 0 - E_m ^0)
The Attempt at a Solution
a)
E_1 ^1 = < (1 | H' | (1 >
0 0
0) 0)
I am not sure how to deal with this as I just get zeroAny help pushing me in the right direction would be appreciated
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