33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2015, Deserno
12th problem sheet, due on Wednesday, April 22nd
34. Occupation number uctuations in the free ideal Fermi- and Bose-gas (5 points)
The occupation numbe

33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2015, Deserno
4th problem sheet, due on Wednesday, February 11th
11. Another inequality just for good measure! (6 points)
a) Let p(x) and p0 (x) be two continuous pr

33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2015, Deserno
11th problem sheet, due on Wednesday, April 15th
31. A single particle in a box (5 points)
Consider a single quantum particle of mass m conned to an ot

33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2015, Deserno
3rd problem sheet, due on Wednesday, February 4th
8. A few more intriguing inequalities, all of which follow from Jensens inequality (12 points)
a) War

33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2015, Deserno
1st problem sheet, due on Wednesday, January 21st
1. Pairwise and mutual independence (3 points)
We ip a fair coin twice and see whether it falls head

33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2015, Deserno
5th problem sheet, due on Wednesday, February 18th
14. Three very simple Legendre transforms (4 points)
The Legendre transform f (p) of a function f (x

33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2015, Deserno
8th problem sheet, due on Wednesday, March 25th
22. Equipartition theorem (4 points)
Consider a Hamiltonian H(cfw_p, q) on phase space. Let xi be any o

33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2015, Deserno
7th problem sheet, due on Wednesday, March 4th
20. A thermodynamic derivation of the barometric height formula (6 points)
As a simplied model of our at

33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2015, Deserno
6th problem sheet, due on Wednesday, February 25th
16. Maximum work from a temperature difference (6 points)
Suppose we have two buckets of water with

33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2015, Deserno
10th problem sheet, due on Wednesday, April 8th
27. Equivalent characterizations of pure quantum states (4 points)
If we have a normalized state vector

33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2015, Deserno
13th problem sheet, due on Wednesday, April 29th
37. Non-relativistic white dwarf (12 points)
A white dwarf is a star in which the degeneracy pressure

33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2015, Deserno
2nd problem sheet, due on Wednesday, January 28th
4. Transformation theorem for probability densitiesprescription strength (5 points)
Let X > 0 be a co