hw03 - Introduction to Quantum and Statistical Mechanics...

Info iconThis preview shows pages 1–2. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Introduction to Quantum and Statistical Mechanics Homework 3 Prob. 3.1. Find the following commutators. Remember that when the commutator of two operators does not vanish, it implies that the two operators cannot be determined with uncertainty simultaneously (a generalization of the Uncertainty Principle) (a) )] ( , [ x V x , where 2 2 2 1 x m V = with m being the mass and the angular frequency later introduced in harmonic oscillators. (4 pts) (b) )] ( , [ x V p , where V is the same as in (a). (4 pts) (c) ] , [ 2 p p (4 pts) (d) ] , [ x p p x (4 pts) Prob. 3.2 For the momentum operator p , (a) Write down the explicit form of p in the x and k spaces. (4 pts) (b) What are the eigenvalues and eigenfunction in the x space? (5 pts) (c) What are the eigenvalues and eigenfunctions in the k space? (5 pts) (d) Reconcile why it is equivalent to evaluate p in the x or k space for any arbitrary wavefunction (x,t) , i.e., k x A p A p | | |...
View Full Document

Page1 / 2

hw03 - Introduction to Quantum and Statistical Mechanics...

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