test3b - Physics 463 - Final Exam: This exam is to be...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 463 - Final Exam : This exam is to be turned in 24 hours after it is received. In solving the following problems you may use any notes, homework sets, and/or solutions accumulated during the semester, one quantum mechanics textbook (including all volumes of a multi-volume set such as Cohen-Tannoudji, et al.), and one mathematical reference. Your score will be based upon your 5 highest scores to the following 6 problems. 1. Use the variational method to estimate the ground-state energy of an electron con f ned to the region x [0 ,L ] by an in f nite square-well potential to which an electric f eld E = E 0 ˆ x has been applied. Choose a family of trial states that satisfy appropriate boundary conditions at the edges of the well. 2. The wave function of a particle subjected to a spherically symmetric potential V ( r ) is given by ψ ( ~ r )=( x + y +3 z ) f ( r ) . (a) Is ψ an eigenfunction of L 2 ? If so, what is the eigenvalue? If not, what values can be obtained if L 2 is measured? (b) If L z is measured, what values can be obtained and with what probabilities? (c) Suppose it is somehow known that ψ ( ~ r ) is an eigenstate of H . Indicate how one may determine V ( r ) . 3.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/19/2010 for the course PHYSICS ph 463 taught by Professor Paule. during the Fall '10 term at Missouri S&T.

Page1 / 2

test3b - Physics 463 - Final Exam: This exam is to be...

This preview shows document pages 1 - 2. Sign up to view the full document.

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