# Lect12 - Lecture 12 Particle in 1D boxes Simple Harmonic...

This preview shows pages 1–6. Sign up to view the full content.

Lecture 12, p 1 Lecture 12: Particle in 1D boxes, Simple Harmonic Oscillators U →∞ U →∞ x n=0 n=1 n=2 n=3 U(x) ψ (x)

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

View Full Document
Lecture 12, p 2 This week and last week are critical for the course: Week 3, Lectures 7-9: Week 4, Lectures 10-12: Light as Particles Schrödinger Equation Particles as waves Particles in infinite wells, finite wells Probability Uncertainty Principle Next week: Homework 4 covers material in lecture 10 – due on Thur. Feb. 17. We strongly encourage you to look at the homework before the midterm! Discussion : Covers material in lectures 10-12. There will be a quiz . Lab: Go to 257 Loomis (a computer room). You can save a lot of time by reading the lab ahead of time – It’s a tutorial on how to draw wave functions. Midterm Exam Monday, Feb. 14. It will cover lectures 1-11 and some aspects of lectures 11-12. Practice exams: Old exams are linked from the course web page. Review Sunday, Feb. 13, 3-5 PM in 141 Loomis. Office hours: Feb. 13 and 14
Lecture 12, p 3 Properties of Bound States Properties of Bound States Several trends exhibited by the particle-in-box states are generic to bound state wave functions in any 1D potential (even complicated ones). 1: The overall curvature of the wave function increases with increasing kinetic energy. 2: The lowest energy bound state always has finite kinetic energy -- called “zero-point” energy. Even the lowest energy bound state requires some wave function curvature (kinetic energy) to satisfy boundary conditions. 3: The n th wave function (eigenstate) has (n-1) zero-crossings. Larger n means larger E (and p), which means more wiggles. 4: If the potential U(x) has a center of symmetry (such as the center of the well above), the eigenstates will be, alternately, even and odd functions about that center of symmetry. ψ - = 2 2 2 2 ( ) for a sine wave 2 2 d x p m dx m ψ (x) 0 L n=1 n=2 x n=3

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

View Full Document
Lecture 12, p 4
The wave function below describes a quantum particle in a range x: 1. In what energy level is the particle? n = (a) 7 (b) 8 (c) 9 2. What is the approximate shape of the potential U(x) in which this particle is confined? ψ(

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 / 24

Lect12 - Lecture 12 Particle in 1D boxes Simple Harmonic...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online