Physics 3220 Quantum Mechanics 1 Fall 2008 Problem Set #4
Due Wednesday, September 17 at 2pm Problem 4.1: Stationary state in the infinite square well. (20 points) The infinite square well has the potential V (x) = 0 , = 0 x a, otherwise , (1) (2)
and the
University of Colorado, Department of Physics PHYS3220, Fall 09, HW#4 due Wed, Sep 16, 2PM at start of class 1. (Griffiths, problem 1.7, 15 pts) Prove the Ehrenfest theorem d < px > V = - dt x (1)
where the potential V is a real quantity. (This theorem te
Physics 3220 Quantum Mechanics 1 Fall 2008 Problem Set #4
Due Wednesday, September 17 at 2pm Problem 4.1: Stationary state in the infinite square well. (20 points) The infinite square well has the potential V (x) = 0 , = 0 x a, otherwise , (1) (2)
and the
PHYS 3220, Fall 09, Homework #1
due Wed, Aug 26, at 2PM (bring in to class) On all homework assignments this term, please show your work and explain your reasoning. We try to grade for clarity of explanation as much as we do for mere "correctness of final
University of Colorado, Department of Physics PHYS3220, Fall 09, HW#5 due Wed, Sep 23, 2PM at start of class 1. A few more properties of Hermitian operators (total: 10pts) a) Show that the sum of two Hermitian operators is a Hermitian operator. ^ b) Suppo
Wave Optics-1
Wave Nature of Light
Light is a wave, an electromagnetic wave. The wavelength of visible light is very small. Visible light: = 400 nm (violet) 700 nm (red) c=f , f=c/ , =c/f Wave-like effects are difficult to detect because of the small wave
Wave Functions and Probability Pretest
Name: _ CU ID: _ For questions 1 and 2 below, you are given a particular (physically reasonable) quantum ( ) x (, ) f x c x e mechanical wave function, ,t of the very specific form t = ( )it where f(x is a real funct
Quantum I (PHYS 3220)
concept questions
Phys3220, U.Colorado at
3-D
Consider a particle in 3D. Is there a state where the result of position in the y-direction and momentum in the z-direction can both be predicted with 100% accuracy?
A) Yes, every state B
WAVE PACKETS I: Localized wave functions A. At time, t = 0, a free particle in one dimension has the wave function shown at right: 1. How do the probabilities of finding the particle very close (within a very small distance dx) to x = A, B, C, and D compa
PHYS 3320
Week 6
Tutorial Energy and the art of sketching wave functions
Goals this week: 1. Developing intuition about the curvature and general behaviours of wave functions for bound states. (LG: Math/phys connection, sketching, checking) 2. Classical l
Energy and the Art of Sketching Wave Functions I: Sketching wave functions A. Review: The figure to the right shows an infinite square well potential (V = 0 from -L/2 to L/2 and is infinite everywhere else). 1. Write down the formula for the energies of t
Monday 8/25/08 On board: Steven.pollock@colorado.edu and oliver.dewolfe@ www.colorado.edu/physics/phys3220 Exam dates: Tuesday 7-9:30 pm, 9/30 & 11/11 HW due on Wed! Office hours: Fri, Mon, Tues (figure out good times) Reading: Griffiths Preface and 1.1-1
Faculty Disagreement about the Teaching of Quantum Mechanics
Michael Dubson1, Steve Goldhaber1,2, Steven Pollock1, and Katherine Perkins1,2
1
Department of Physics, UCB 390, University of Colorado at Boulder, Boulder CO 80309 2 Science Education Initiativ
SJP QM 3220 Formalism 1
The Formalism of Quantum Mechanics: Our story so far . State of physical system: normalizable ( x, t )
^ ^ Observables: operators x , p =
^ ,H i x
Dynamics of : TDSE i
^ = H t
^ To solve, 1st solve TISE: H = E
Solutions are st
PHYS 3320
Week 2
Tutorial Wave functions and probability
Goals this week: 1. Developing intuition about the time dependence, and complex nature of, the spatial wave function, including stationary states and superposition states (LG: Math/phys connection,
SJP QM 3220 3D 1
AngularMomentum(warmupforHatom) Classically,angularmomentumdefinedas(fora1particlesystem) y m x O Note: definedw.r.t.anoriginofcoords. (InQM,theoperatorcorrespondingtoLxis accordingtoprescriptionofPostulate2,part3.) Classically,torquedefi
PHYS 3220 - Quantum I
Student Learning Difficulties
This document provides a brief summary of common student learning difficulties which have been previously published in studies of student learning in upper-division quantum mechanics. Because many of the
SJP QM 3220 3D 1
Angular Momentum (warm-up for H-atom) Classically, angular momentum defined as (for a 1-particle system) y m Lrp ^ ^ ^ x y z p = mv r = x y z x px p y pz O Note: L defined w.r.t. an origin of coords. ^ ^ L = x ( yp z - zp y ) + y ( zp x -
S-1
Spin
Recall that in the H-atom solution, we showed that the fact that the wavefunction (r) is single-valued requires that the angular momentum quantum nbr be integer: l = 0, 1, 2. However, operator algebra allowed solutions l = 0, 1/2, 1, 3/2, 2. Exp
Lecture notes (these are from ny earlier version of the course - we may follow these at a
slightly different order, but they should still be relevant!) Physics 3220, Steve Pollock.
Basic Principles of Quantum Mechanics
The first part of Griffith's Ch 3 is
Lecture notes (these are from ny earlier version of the course we may follow these at a
slightly different order, but they should still be relevant!) Physics 3220, Steve Pollock.
Basic Principles of Quantum Mechanics
The first part of Griffith's Ch 3 is
Here were some Chapter by Chapter content learning goals SJP posted for students before midterms: Chapter 1: Statistical interpretation: this is our introduction to what " tells you: you should know how to use it to figure out probability of measurement.