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7. The wave function of a system is given as y = 3/4t sin 0 sin o. Calculate
(wIL,L.\W).

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(5) The wave function for a particle is given by: (x) = Ae-=/L for r 2 0, where A and L are constants, and L > 0. b(x) = 0 for r < 0. (a) Find the value of the constant A, as a function of L. A useful integral is: fe-K=dx = -ke-K, %3D where K is a constant. (b) What is the probability of finding the particle in the range –10 L < x< -L? (c) What is the probability of finding the particle in the range 0
The expectation value of a function f(x), denoted by (f(x)), is given by (f(x)) = f(x)\(x)|³dx +00 Yn(x) = where (x) is the normalised wave function. A one-dimensional box is on the x-axis in the region of 0 ≤ x ≤ L. The normalised wave functions for a particle in the box are given by -sin -8 Calculate (x) and (x²) for a particle in the nth state. n = 1, 2, 3, ....
The amplitude of a scattered wave is given by 1 S(0) = (21 + 1)exp[id] sin 3i P(cos 0), l=0 where e is the angle of scattering, I is the angular momentum, ik is the incident momentum, and & is the phase shift produced by the central potential that is doing the scattering. The total cross section is oiot = S IS(O)²a2. Show that 47 Otot = FL(21+ 1)sin² § . %3D0