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Unformatted text preview: a n , the state vector becomes the corresponding eigenvector A n . “Collapse!” 4 If | ψ i is the initial state, the probability that a measurement collapses it to A n with value a n is: P ( a n ) = |h ψ | A n i| 2 where | ( a + bi ) | 2 = a 2 + b 2 5 Superposition: | ψ i = c 1 | + y i + c 2 |-y i = | + y ih + y | ψ i + |-y ih-y | ψ i (Be able to derive 2nd equality.) The c i ’s are not the eigenvalues!!! 6 Any | ψ i can be decomposed into energy eigenvectors (they “span” the space): | ψ ( t = ) i = c 1 | E 1 i + c 2 | E 2 i + ··· At time t : | ψ ( t ) i = c 1 e-iE 1 t / ~ | E 1 i + c 2 e-iE 2 t / ~ | E 2 i + ··· ( ~ ≡ h / 2 π )...
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- Spring '11
- Quantum Physics, Eigenvalue, eigenvector and eigenspace, eigenface, state vector, state vector |ψ, Nicholas Jarjour