Phys 622: Problem Set 1
August 30, 2015
Problem (1)[Optional]. Plancks radiation law using energy quantization.
Assume that the radiation in a box is described by a scalar potential (r),
where r = (x, y, z) is position in a box. The Hamiltonian fo
Phys 622: Problem Set 2
September 11, 2015
Problem (1). Simple bra-ket exercises.
Using bra-ket properties, given an operator A of the form
i |i i |,
where |i is an orthonormal basis show that
f (i )|i i |.
f (A) =
[Hint: proceed rs
Phys 622: Problem Set 3
September 18, 2015
Problem 1: Unitary operators:
(a) Suppose Rmn = m|U |n is the matrix representation of a unitary operator U in an orthonormal basis cfw_|n D the show that R is a unitary matrix
i.e. RR = 1.
(b) If U i
Phys 622: Problem Set 4
September 30, 2014
Problem (1)Position and momentum operators.
(a) By expanding the momentum states |p in a complete set of position
eigenkets |x , show that if
dpi (p (p)|p .
(b)Show that the
1. Arfken Chapter 6 : 1.10(a), 1.15(a)and (d), 2.1(a), 2.2, 2.3, 2.8, 7.1(a), 7.3(a)
2. Define a cut in the complex z plane to make z 1/3 single valued. Evaluate
3. Define cuts in the complex z plane
1. Arfken Chapter 6 : 3.3, 4.1, 4.3, 4.4
2. If a function f (z) is analytic on and within a closed contour C show that unless
it is a constant it takes on its maximum value on C .
Hint: Assume that f (z) takes its