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7 15 points straightforward but part c is probably longer...

Question: 7 15 points straightforward but part c is probably longer...

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7. (15 points) (Straightforward, but part (c) is probably longer) Consider a particle in the infinite square well with the following wavefunction at t 0: V (x, 0) A (2(x)is (x)) for 0 3ISa V (x,0)0, otherwise. where ψ(x) is the nth solution to the time-independent Schrodinger equation, as discussed in the class. (a) Find the constant A that will normalize Ψ at t-0, will this constant normalize Ψ (x, t) for all time, t? (b) Find Ψ(x,t). (c) At time, t--0, find (z), (p), Oz and Op. Verify the uncertainty relation. σ rneans the standard deviation of a given quantity. (d) At time, t-0, find(E) and σΕ. (e) At time, 0, what is the probability that a measurement of the energy system yields E2 ma

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