Lecture_18

# Lecture_18 - PHYS 342 all 2011 Fall 2011 Lecture 18...

This preview shows pages 1–5. Sign up to view the full content.

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

View Full Document

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.

Unformatted text preview: PHYS 342 all 2011 Fall 2011 Lecture 18: Confidence Building Examples: he Hydrogen Atom the Hydrogen Atom e- , m U(r) Lecture 18 1 Probability Density Probability Density 2 * In 1-D, the probability of finding a particle between x and x+dx is * ( ) ( ) x x d x n 3 the probability of finding a Implications for units In 3-D, the probability of finding a particle between (r, θ , φ ) and of Ψ (r+dr, θ +d θ , φ +d φ ) is * ( , , ) ( , , ) r r dV 2 The volume element dV in spherical coordinates The paralellpiped approaches a pp rectangular box as dr → 0, d θ → 0, d φ → 0, so the volume element just http://www.netcomuk.co.uk/~jenolive/polar.html is just 3 Working it out 2 sin sin dV dr rd r d r dr d d Probability of finding electron at r, θ , φ is P(r, θ , φ ) : 2 , , , , , , , , , 2 2 ( , , ) ( , , ) ( , , ) ( ) ( , ) ( ) ( , ) ( ) n m n m n m n m m P r r d V r R r Y R r 2 2 2 2 , , , ( , , ) ( ) ( , ) sin ( ) n m m P r r R r dr d d Probability of finding electron between shell of radius r and a shell of radius r+dr: 2 2 2 2 , , , ( ) ( ) ( , ) sin ( ) n m m P r r R r dr d 2 2 2 2 ) ( ) ( ) ( ) ( ) d r r R r dr P r dr if and are normalized , , , , 2 2 ( ) ( ) ( ) ( , ) ( ) n n m m P r r R r dr P r dr if and are normalized Expectation value of some function f(r): 2 , , ( ) ( ) ( ) ( ) ( ) ( ) ( ) n n f r f r P r dr f r r R r...
View Full Document

## This note was uploaded on 12/08/2011 for the course PHYS 342 taught by Professor Staff during the Fall '08 term at Purdue.

### Page1 / 14

Lecture_18 - PHYS 342 all 2011 Fall 2011 Lecture 18...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online