237module5

237module5 - Quantum Mechanics I Module 5 Try your hand at...

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Quantum Mechanics I - Module 5 Try your hand at the problems below. These are meant to be a review and you should be ready to answer any of them should they appear on an upcoming quiz! 1. There are two theorems concerning commutators that can come in handy. If A, B, and C are operators, then: [ AB,C ] = A [ B,C ] + [ A,C ] B. Also, for any operators A and B: [ A,B ] = - [ B,A ] . (a) Work out the commutator [ x,p 2 x ] by the brute force method, con- structing the square of the momentum operator and writing it all out. (b) Work out the same commutator by using the above theorems and the fact that [ x,p x ] = i ~ . (c) What can you say about the uncertainty relations involving Δ x and Δ p x ? 2. Consider the infinite square well extending from x = 0 to x = L . (a) Write down a normalized expression for the fifth state ψ 5 ( x ) that is a solution of the time independent Schroedinger equation. (b) Write down an expression for the full solution of Schroedinger’s equa-
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This document was uploaded on 09/10/2009.

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237module5 - Quantum Mechanics I Module 5 Try your hand at...

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