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
Final Exam
13 June 2017
Physics 130a
Spring, 2017
University of California, San Diego
Open all Hard Copy Books
Not Open Friends or Open Internet Time limit: 3 hours total.
Physics 130a, 2017 students:
In allowing this exam to be a take-home exam distribut
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