4. For the eigenfunctions y.(x) of the infinite square well with walls at x = 0 and x = L, a. Show that = L/2 and b. Show (x²) = 12 L² 3 2л²² c. What is the uncertainty Ax as a function of n. Does the uncertainty grow or shrink as n increases. d. What is the uncertainty Ax when n goes to infinity.
4. For the eigenfunctions y.(x) of the infinite square well with walls at x = 0 and x = L, a. Show that = L/2 and b. Show (x²) = 12 L² 3 2л²² c. What is the uncertainty Ax as a function of n. Does the uncertainty grow or shrink as n increases. d. What is the uncertainty Ax when n goes to infinity.
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Transcribed Image Text:4. For the eigenfunctions y.(x) of the infinite square well with walls at x = 0 and x = L,
a. Show that <x> = L/2 and
b. Show
(x²) = 12
L²
3
2л²²
c. What is the uncertainty Ax as a function of n. Does the uncertainty grow or shrink as n increases.
d. What is the uncertainty Ax when n goes to infinity.
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