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1. A particle in the infinite square well has the initial wave function
L
2Ax,
0<x<키
Y(x, 0) =
L
| A(L – x), <xs
-
otherwise,
for some constant A. This wave function is sketched below.
v (x, 0)
2AL
L
(a) Determine the constant A by normalizing 4(x, 0).
(b) Find Y(x, t).
(c) Calculate the probability that a measurement of the energy would yield the values (i) E1,
(ii) E2, and (iii) E3.
(d) Calculate the average position, (x), of the particle at t = 0.
(e) Calculate the average momentum, (p), of the particle at t = 0.
(f) Calculate the average energy, (E), of the particle. (Note: E-1 sin? () = 5-)
n=1
n²

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