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Unformatted text preview: Phys3220, U.Colorado at Quantum I (PHYS 3220) concept questions 3D Phys3220, U.Colorado at Consider a particle in 3D. Is there a state where the result of position in the ydirection and momentum in the zdirection can both be predicted with 100% accuracy? A) Yes, every state B) Yes, at least one state (but not all) C) No, there is no such state D) Yes, but only for free particles E) Yes, but only for a spherically symmetric potential (not just free particles) 94 Phys3220, U.Colorado at Is the 3D wave function an eigenfunction of A) Yes B) No u ( x , y , z ) = 2 a 3 2 sin n x x a sin n y y a sin n z z a 85 H x = h 2 2 m 2 x 2 ? Phys3220, U.Colorado at For the particle in a 3D box, is the state (n x , n y , n z ) = (1, 0, 1) allowed? A) Yes B) No 82 Phys3220, U.Colorado at The ground state energy of the particle in a 3D box is What is the energy of the 2 nd excited state? A) 4 B) 5 C) 6 D) 8 E) 9 1 2 + 1 2 + 1 2 ( 29 h 2 2 2 ma 2 = 3 . 83 Consider three functions f(x) , g(y), and h(z). f(x) is a function of x only, g(y) is a function of y only, and h(z) is a function of z only. They obey the equation f(x) + g(y) + h(z) = C = constant. What can you say about f, g, and h? A) f, g, and h must all be constants. B) One of f, g, and h, must be a constant. The other two can be functions of their respective variables. C) Two of f, g, and h must be constants. The remaining function can be a function of its variable. 80 Consider three functions f(x) , g(y), and h(z) which obey the equation f(x) + g(y) + h(z) = C = constant. How many of the functions must be constant? A) f, g, and h must all be constants. B) One of f, g, and h, must be a constant. C) Two of f, g, and h must be constants. 81 Phys3220, U.Colorado at In the 3D infinite square well, what is the degeneracy of the energy corresponding to the state (n x , n y , n z ) = (1, 2, 3)? A) 1 B) 3 C) 4 D) 6 E) 9 84 In Cartesian coordinates, the normalization condition is In spherical coordinates, the normalization integral has limits of integration: E) None of these d x d y d z 2 = 1. 100 A) dr + d 2 d K B) dr + d 2 d K C) dr + d 2 d 2 K D) dr + d d K Phys3220, U.Colorado at Separation of variables has gotten us to Is there anything we can say about the sign of the constant c in that equation? A) c must be 0 B) c must be 0 C) c can be + or , but it cannot be 0 D) Cant decide without knowing more: ( whats the potential, what are the boundary conditions for our particular problem?) 1 ( ) d 2 ( ) d 2 =  c angular momentum The angular stationary state wave fns for central potentials are: If the quantum number m is large , what can you conclude about the wave function and probability density as you vary...
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 Fall '08
 STEVEPOLLOCK
 Angular Momentum, Momentum, NZ, Hermitian, Ylm

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