Download Homework 5 { PHYS 5450

Homework 5 { PHYS 5450
[1] We consider the innite square
well of width a.
(a) Find the energies En and normalized wave functions n of the stationary states in terms of the quantum
number n
(b) Calculate the momentum representations n(p) of the stationary states. Manipulate your expression so
as to make it appear as a sum of two sinc functions: sinc(u) = sinu(u) .
(c) Make a graphical representation of the momentum probability densities for n = 1 and n = 2.
(d) Sketch the momentum probability densities for a large value of n.
(e) Using n(p) evaluate the expectation value of the momentum p
(f) Using n(p) write the expectation vale of p2 as an integral you will not attempt calculating.
(g) Using (x), calculate the expectation value of p2.
[2] Consider the wave
function j (t = 0) >= p12 [j1 > +j2 >].
(a) Write j (t) > using the Bohr frequency !21 = E2 h E1
(b) Calculate < x > (t). The calculation will be easier if consider x'=x-a/2 instead of x directly. Easier is
better.
(c) Calculate < H > and < H 2 > to estimate H the standard deviation of the energy. Then calculate
H 2!