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Unformatted text preview: Chemistry 550 / 475 Homework Assignment #3 due: Friday, October 14th at 5:00 pm Readings : Chapter 7 in Levine Problem 1 - Free particle. Find the eigenfunctions of the free particle Hamiltonian a. H = p 2 x / 2 m in one dimension. What are its allowed eigenvalues? Does this make physical sense? Explain. b. H = p 2 / 2 m in three dimensions. What are its allowed eigenvalues? Does this make physical sense? Explain. Problem 2 - Particle in a three-dimensional box. Solve the time-independent Schr odinger equation for a single particle subjected to the external potential energy V ( x ) = braceleftbigg , (0 , , 0) < ( x,y,z ) < ( L x ,L y ,L z ) , elsewhere using the method of separation of variables. Normalize the resulting solution so that 1 = integraldisplay box Prob( x,x + dx ; y,y + dy ; z,z + dz ) d 3 x and compute the allowed energies. Note that the only differences between problem 1 b and this problem are the boundary conditions. Prove that the resulting wave functions arethis problem are the boundary conditions....
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- Fall '11