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Unformatted text preview: ECE 306 Homework Set #8 Spring 2005 (Due Wednesday, April 6, 2005.) 1. A particle is known to be in a state such that L2 = 22. It is also known that measurement of Lz will yield the value + with the probability 1/3 and the value with the probability 2/3. a. What is the normalized wave function (, ), of this particle in terms of the Yl m ( , ) functions? b. What is the expectation value < Lz >, of the zcomponent of the angular momentum of this particle? 2. The wave function of a particle of mass m moving in a potential well is, at a particular time t: ( x, y , z ) = ( x + y + z )e  x2 + y 2 + z 2 a. Write in the spherical coordinate system, (r, , ) in normalized form b. What is the probability that measurement of L2 and Lz gives the values 22 and 0, respectively? 3. Consider a hydrogen atom in the following mixed state at t = 0: (r , , ) = 3R32 (r )Y20 ( , ) + R21 (r )Y11 ( , ) a. Normalize the wave function. b. Is the atom in a stationary state (i.e. an eigenfunction of the Hamiltonian). Explain briefly. c. What is the expectation value of the energy at t > 0? d. What is the expectation value of L2 and Lz at t = 0? e. What is the uncertainty of Lz in this state? = L  L z 2 z [ 1 2 2 ...
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This homework help was uploaded on 10/25/2007 for the course ECE 3060 taught by Professor Tang during the Spring '05 term at Cornell.
 Spring '05
 TANG

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