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Unformatted text preview: Physics 828: Problem Set VII Dr. Stroud Due Thursday, February 28 by 11:59 P. M. Each problem is worth 10 pts. unless otherwise specified. 1. Shankar, problem 18.2.2. 2. Shankar, problem 18.2.6. 3. Density of free particle states in one dimension. In class, I showed that for a free particle of mass m , the density of states in energy ( E ) = AE 1 / 2 , where E is the energy, and A is a constant. We also derived the value of the constant. If the particle is spinless, we found that A = V (2 m/ h 2 ) 3 / 2 / (4 2 ), where V is the volume of the system, and ( E ) is defined by the statement that the number of free particle states between E and E + dE is ( E ) dE . Now carry out the same calculation for a free particle of mass m in 1D. Again, as in class, use periodic boundary conditions to find the allowed values of k in a system of length L along the x axis. Show that the density of states in this case, assuming spinless particles, is ( E ) = L 2 parenleftbigg 2 m h...
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