1. A particle in the infinite square well has the initial wave function 2Ax, 0
1. A particle in the infinite square well has the initial wave function 2Ax, 0
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Can you do all parts please.
Transcribed Image Text:1. A particle in the infinite square well has the initial wave function
osrs
L
0<x<
2Ax,
Ф(х, 0) —
L
| A(L – x), <x<L
otherwise,
for some constant A. This wave function is sketched below.
V (x,0)
2AL
3
L
3
L
(a) Determine the constant A by normalizing Y(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.
1
(f) Calculate the average energy, (E), of the particle. (Note: En=1 sin?
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