130a Homework 2, due 4/17
1. A crystal is a lattice array of atoms, with separation a. An incident particle can scatter
o of one or another neighboring atom. The dierence in the path length between the
two scattered paths is 2a cos , where is the angle of
130a Homework 4, due 5/1
1. Shankar 1.8.10 (page 46).
2. Recall the denition of adjoint: if A| |A , then A | = |A | , for any |
and | . Recall the denition of Hermitian: A is Hermitian A = A .
(a) Show that. if A and B are Hermitian, then so is (A + B )n
130a Homework 3, due 4/24
1a. Prove (in momentum space) that xn = 0, for all odd n, whenever (p) is real.
1b. Show that, if (x) has mean momentum p = p, then eip0 x/h (x) has mean momen
tum p = p + p0 .
2. Suppose that
A for p0 b < p < p0 + b
0 otherwise,
130a Homework 1, due 4/10
1. Consider the harmonic oscillator: a particle of mass m is on a frictionless surface, and
connected to a spring. Let x be the displacement of the mass from equilibrium. The
spring provides the restoring force Fx = x.
(a) Write
130a Homework 5, These are practice problems, you dont need to turn them in.
1. Evaluate the following quantities:
(a) p|x2 |x .
(b) p|p2 |x .
(c) x|px|p
(d) x |x2 |x .
2. Write the following in the bra-ket notation. Simplify the result as much as possibl
130a Homework 6, Due May 22, 2008.
1. Consider the particle of mass m in the innite potential well. Suppose that
1
| (t = 0) = |En=1 +
3
2
|En=2 .
3
(a) Use the fact that | (t) = exp(iHt/ )| (t = 0) to write an expression for
h
(x, t) = x| (t) , as an ex
Sample Midterm 1
May 7, 2012
Physics 130A
1. Calculate the DeBroglie wavelength for
(a) a proton with 10 MeV kinetic energy,
(b) An electron with 10 MeV kinetic energy, and
(c) a 1 gram lead ball moving with a velocity of 10 cm/sec (one erg is one gram cm
6/2/08 Homework 8 Problems do not need to be turned in.
1. Shankar 9.4.3
2. Consider a particle in a 3d box:
V ( x) =
0 if 0 x L and 0 y L and 0 z L
otherwise
(a) Find the energy eigenvalues and the energy eigenstates (in position space).
(b) What is the
5/22/08 Homework 7 Due May 29, 2007.
1. Consider a quantum mechanical system which has only two available states, i.e. the
ket | is a vector in a K = 2 dimensional, complex vector space. This space has a
complete, orthonormal basis of kets |ei , for i = 1
L.J. Sham
June 8, 2009
Physics 130A Final Examination Solutions
PRINT your name and attach only this page to the front of your bluebook.
Name: Do problem 1 and choose ONLY FOUR from problem 2 to problem 6. (Cross out one column from problem 2 to problem 6
L.J. Sham
May 31, 2009
Physics 130A Sample Final Examination
PRINT your name and attach the entire set of examination questions to the front of your bluebook.
Name: Do problem 1 and choose ONLY FOUR from problem 2 to problem 6. (Cross out one column from