This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Quantum Mechanics I  Module 3 Getting Started 1. The ordinary differential equation dψ ( x ) dx = [ ψ ( x )] 2 has the general solution ψ α ( x ) = 1 α x where α can be any real (or complex) number. Examine the sum of two specific solutions, ψ 1 ( x ) = 1 1 x , ψ 2 ( x ) = 1 2 x . (a) Does the new function ψ 1+2 ( x ) = 1 1 x + 1 2 x satisfy the original differential equation? (b) From your knowledge of differential equations, specifically the word “linear”, what is it about the differential equation that causes solu tions to be nonadditive? 2. Fun with Dirac notation! Rewrite each of the expressions using integrals and wavefunctions. (a) h ψ  ψ i = 1 (b) A op  ψ i = a  ψ i (c) h ψ  x op  ψ i Discussion Questions 1. What is the goal of quantum mechanics so far as you can discern from this course? 2. What critical relationships connect the behavior of particles to the behav ior of waves?...
View
Full
Document
This document was uploaded on 09/10/2009.
 Spring '09
 mechanics

Click to edit the document details