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Unformatted text preview: ECE 306 Homework Set #2 Spring 2005 (Due 12 noon, Wednesday, February 9, 2005.) 1. Suppose an electron is confined to a zeropotential region between two impenetrable walls at x = 0 and a for all times. Its initial wave function is given by: a x x a x a x a x < < = , , , ) 3 sin( 2 { ) ( a. Calculate the expectation value of the energy < ^ H > in this state b. Calculate the energy eigen value corresponding to this state. c. What is the time dependence of (x,t)? d. Calculate the uncertainty in the total energy in this state, ^ H . Is the answer what you expect? Explain. 2. Prove the following commutation relationships: a. [A + B,C] = [A,C] + [B,C] b. [A, BC] = [A,B]C + B[A,C] 3. Prove the following commutation relations: a. [ p x , x n ] = i nx n1 b. [ x, p x 2 ] = 2i p x c. From b above, what can you say about the possibility of measuring the position and kinetic energy of a particle in an arbitrary state simultaneously with zero uncertainty in each measurement? ECE 306...
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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 University (Engineering School).
 Spring '05
 TANG

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