HW08 & Solutions

HW08 & Solutions - ECE 306 Homework Set #8 Spring 2005 (Due...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 z-component 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 ...
View Full Document

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.

Page1 / 5

HW08 & Solutions - ECE 306 Homework Set #8 Spring 2005 (Due...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online