PHYSICS 390 Michigan

Statistical Physics Basic Problem: Suppose I have N particles which are distributed into a set of energy states such that the total energy of the particles is fixed to be Etot: ns = N (1) states (2) states n E s s =E tot Question: What is the

Physics 390: Homework 1 For full credit, show all your working. 1. Problem 3-8 from Tipler & Llewellyn. 2. Planck\'s law: As we saw in class, the average energy of a mode in Planck\'s quantized theory of the radiation in a cavity is given by E= hf -nh

Physics 390: Homework 2 1. Problem 4-49 in Tipler & Llewellyn. Note in part (d) that Rutherford cross section refers not to the cross section in the rst part of the question but to Rutherfords original cross section from page 154 and Equation 4-3. 2.

Physics 390: Homework 3 For full credit, show all your working. 1. De Broglie waves: As we discussed in class, the typical kinetic energy of particles such as the molecules in a gas, at temperature T in Kelvin, is kT, where k is Boltzmanns constant.

Physics 390: Homework 4 For full credit, show all your working. 1. Problem 6-16 in Tipler & Llewellyn. 2. Uncertainty relation: Suppose that we measure the uncertainty in position and momentum by their standard deviations: x = x2 - x 2 , p = p2 - p 2

Physics 390: Homework 5 For full credit, show all your working. 1. Problem 7-10 in Tipler Llewellyn. 3. Ground state of hydrogen: We claimed that the ground-state wave function of the hydrogen atom is 100 (r)

Physics 390: Homework 6 For full credit, show all your working. 1. Quantum mechanics of many particles: The neutron and the neutral pion are two subatomic particles with no charge, so that they neither electrically repel nor attract other particles.

Physics 390: Homework 7 For full credit, show all your working. 1. Atoms in a magnetic field: A Lithium atom has its outer electron in the 3p state. (a) What is the value of the orbital angular momentum quantum number for this electron? What is the

Physics 390: Homework 8 For full credit, show all your working. 1. Problem 10-4 in Tipler & Llewellyn. 2. Madelung constant for a 1D system: Consider a one-dimensional model of an ionic crystal consisting of an infinite line of ions spaced r apart, w