Phys 402 Spring 2009 Homework 9 Due Friday, May 1, 2009 @ 9 AM 1. Griffiths, 2nd Edition, Problem 5.29 Follows the lectures on Bose-Einstein condensation 2. Griffiths, 2nd Edition, Problem 5.16 Fermiology 3. Griffiths, 2nd Edition, Problem 5.37. Hint: To calculate the degeneracy of state En of the 3D harmonic oscillator you have to answer the question: “How many ways can we add three non-negative integers to get a particular sum n?”Physics 402 Spring 2009 Prof. Anlage Discussion Worksheet for April 29, 2009 1. Macroscopic quantum model of superfluidity. To described the condensed phase of superfluid 4He, we posit the existence of a single quantum wavefunction that describes the collective behavior of all the atoms in the ground state: )(00)()(riernrrrrθψ=, where 200)()( rrnrrψ= is the local density of condensed particles, and )(rrθis the spatially varying phase. Using the definition of probability current (Eq. [4.193]), and re-interpreting it as the mass current, find the superfluid velocity svrin the expression . svnJrr0=2. When superfluid 4He is constrained to flow in a circular channel, the circulation maintains itself with no dissipation. Show that the values of the circulation κare restricted to the discrete quantum valuesmhnldvs=•=∫rrκ, where K,2,1,0
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