(a) Find the momentum space wave function n (p,t) for the nth stationary state of the infinite square well (b) Find the probability density n (p,t) 2 Graph this function, for n 1, n 2, n 5, and n 10 What are the most probable values of p, for large n Is this what you would have expected Compare you...

a b Noting that we have From the formula it looks as though the maxima should occur at p na though s ...

(a) Find the momentum-space wave function n (p,t) for the nth stationary state of the infinite...

Question:

(a) Find the momentum-space wave function Φ_n (p,t) for the nth stationary state of the infinite square well.

(b) Find the probability density |Φ_n (p,t)|². Graph this function, for n = 1, n = 2, n = 5, and n = 10. What are the most probable values of p, for
large n? Is this what you would have expected? Compare your answer to Problem 3.10.
(c) Use Φ_n (p,t) to calculate the expectation value of p², in the nth state. Compare your answer to Problem 2.4.

Problem 3.10

Is the ground state of the infinite square well an eigenfunction of momentum? If so, what is its momentum? If not, why not?

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