{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

3063_Exam3_sp06

# 3063_Exam3_sp06 - PHY3063 Spring 2006 R D Field PHY 3063...

This preview shows pages 1–4. Sign up to view the full content.

PHY3063 Spring 2006 R. D. Field Final Exam Page 1 of 7 April 25, 2006 PHY 3063 Final Exam Name_________________ Problem 1 (35 points): Consider an particle with mass m confined within an infinite square well defined by V(x) = 0 for 0 < x < L , V(x) = + otherwise. (a) (5 points): Using Schrödinger’s equation calculate the allowed stationary state eigenfunctions ψ n (x) , where the complete wavefunctions are given by h / ) ( ) , ( t iE n n n e x t x = Ψ ψ . Normalize the eigenfunctions so that the probability of finding the particle somewhere in the box is one. (b) (5 points): Show that the allowed energy levels of the system are, E n = E 0 n 2 , where ) 2 /( 2 2 2 0 mL E π h = is the ground state energy and n = 1, 2, 3, …. Why is n = 0 excluded as a possible energy level? (c) (10 points): Consider the operator, O = (x) op (p x ) op ( i.e. the product of the position operator times the momentum operator). Is the operator O hermitian? Calculate the expectation value of the operator O for the n th stationary state ( i.e. calculate < ψ n |O| ψ n >). (d) (15 points): Suppose the particle in this infinite square well has an initial wave function at t = 0 given by ) / ( sin ) 0 , ( 2 L x A x = Ψ . What is the normalization A ? If you measure the energy of this particle, what is the probability that you will measure the ground state energy E 0 ? V = +infinity V = +infinity Infinite Square Well 0 L x

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

View Full Document
PHY3063 Spring 2006 R. D. Field Final Exam Page 2 of 7 April 25, 2006 PHY 3063 Final Exam Name_________________ Problem 1 Scratch Paper
PHY3063 Spring 2006 R. D. Field Final Exam Page 3 of 7 April 25, 2006 Problem 2 (35 points): Consider the case of two non-interacting particles both with mass m

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 7

3063_Exam3_sp06 - PHY3063 Spring 2006 R D Field PHY 3063...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online