CHAPTER 1
1.1 The function and its constraint are
f (x, y )
=
3x2 4xy + y 2 ,
(1)
C (x, y )
=
3x + y = 0.
(2)
According to the method of Lagrange multipliers, we have
(f (x, y ) C (x, y ) = 6x 4y 3 =
Physics 831 Quiz #2 - Friday, October 2
1. Consider a MASSLESS( p = p) three-dimensional gas of spinless bosons which is kept at
temperature T . Solve for the density of Bose Condensation, c (T ). You
Physics 831 Quiz #1 - Friday, Sep. 5
1. Consider 2 non-interacting electrons populating two single-particle levels of energy and .
(a) What is the average energy for T = 0?
(b) What is the entropy for
Physics 831 Quiz #3 - Wednesday, Oct. 14
1. A molecule of mass m has internal excitations consistent with that of a TWO-DIMENSIONAL
harmonic oscillator with tightly packed levels, h < T . Initially, a
Physics 831 Quiz #4 - Monday, Nov. 2
1. Consider a gas of non-relativistic one-dimensional zero-temperature spin-1/2 fermions of mass
m, lling up all states with momenta, pf < p < pf . The system is a
Physics 831 Quiz #7 - Friday, Oct. 17
1. Assume the free energy for a complex eld in ONE dimensions is given by:
F=
dx
1
A |2 + |x |2 .
2
Dene the correlation as
(x) (0)(x) .
Fourier transforms in one
Physics 831 Quiz #5 - Monday, Nov. 9
1. A two-dimensional lattice is made of coupled oscillators that are constrained to move only
within the two-dimensional plane of the lattice. The oscillators have