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Unformatted text preview: t . What is the probability that a measurement of the energy of the system f nds: a) E = E 1 , b) E = E 2 , and c) E = E 3 , where the eigenstate energies are E n = h 2 2 2 mL 2 n 2 ? 4. For a quantum particle moving in a 3D potential, V ( x ) = V ( x, y, z ), which directions, if any, of the particles momentum are conserved if the potential takes the following form: (a) V = ax + by 2 + cz 3 , where the constants, a , b , and c are all positive. (b) V = a arctan( x/L ) (c) V = b exp( y 2 /d 2 ) 5. For which systems characterized by the potentials listed below, do the energy and parity observables have common eigenfunctions? (a) V = e 2 /r ; where r = x 2 + y 2 + z 2 . (b) V = ax + by 2 + cz 3 (c) V = axy 6. Libo f , problems 9.3, 9.25(a), 9.30, 9.34, 9.35....
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