1 / 20

Physics 451

Physics 451. Quantum mechanics I Fall 2012. Sep 21, 2010 Karine Chesnel. Quantum mechanics. Announcements. Homework this week: Thursday Sep 20 by 7pm: HW # 7 pb 2.19, 2.20, 2.21, 2.22. Friday 21: Review - Monday 24: Practice test 1 Plan to work on your selected problem

wendyswan
Download Presentation

Physics 451

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Physics 451 Quantum mechanics I Fall 2012 Sep 21, 2010 Karine Chesnel

  2. Quantum mechanics Announcements • Homework this week: • Thursday Sep 20 by 7pm: • HW # 7pb 2.19, 2.20, 2.21, 2.22 • Friday 21: Review - Monday 24: Practice test 1 • Plan to work on your selected problem • with your group and prepare the solution • to be presented in class (~ 5 to 7 min) Test 1: Mon Sep 24 – Th Sep 27

  3. Note from the TA about homework • Answer the problems completely. A lot of the problems • have multiple parts. For example, they first ask you to do • the derivation, and then ask for a qualitative description, • and finally let you give an analog to something. • Don't just do the math and forget everything else. • 2. Use precise terminology to describe phenomena. • For example, in problem 2.2 of Homework 4, you are • supposed to comment on the concavity/divergence of the • function. Those are the terms I am looking for. •   Don't write something like "the function dies at infinity". • That is a vague expression and it is also unprofessional. Muxue Liu

  4. Pb 2.13 Quantum mechanics Quiz 9a Since the operators a+ and a- are shifting the stationary states from one level to another, and since the stationary states are all orthogonal, the expectations values for x and p on any state will ALWAYS be zero! • True • False

  5. Quantum mechanics Ch 2.3 V(x) x Harmonic oscillator Solving the Schrödinger equation the direct way! (analytic method)

  6. Quantum mechanics Ch 2.3 V(x) General solution Expanding h in power series x Harmonic oscillator Solving the Schrödinger equation the direct way! (analytic method)

  7. Quantum mechanics Ch 2.3 V(x) Is equivalent to: Recursion formula x Harmonic oscillator Solving the Schrödinger equation the direct way! (analytic method)

  8. Quantum mechanics Ch 2.3 V(x) Hermite polynomials x Harmonic oscillator Solving the Schrödinger equation the direct way! (analytic method) Final solution:

  9. Quantum mechanics Ch 2.3 Harmonic oscillator

  10. Quantum mechanics Ch 2.3 Harmonic oscillator n=100

  11. Quantum mechanics Quiz 9b “In quantum mechanics, the energy of a particle is always quantized” • True • False

  12. Quantum mechanics Ch 2.4 Free particle V = 0everywhere

  13. Quantum mechanics Ch 2.4 with General Solution Complete wave function Free particle

  14. Quantum mechanics Ch 2.4 wave travelling in the (-x) direction with speed v wave travelling in the (+x) direction with speed v Velocity of the phase with Free particle Wave function represents a physical wave:

  15. Quantum mechanics Ch 2.4 • Velocity of the phase • Analogy with classical velocity (using the de Broglie formulae) Free particle Talking about velocity

  16. Quantum mechanics Ch 2.4 Individual waves superposition (summation) dispersion function Free particle Normalization • A single wave for a given E is NOT a physical solution! • A superposition of waves IS normalizable! Wave packet

  17. Quantum mechanics Ch 2.4 Pb 2.20 Extension from discrete sum to continuous integration Free particle Wave packet Fourier transform Inverse Fourier transform Plancherel’s theorem

  18. Quantum mechanics Ch 2.4 1. Identify the initial wave function 2. Calculate the Fourier transform 3. Estimate the wave function at later times Pb 2.21, 2.22 Free particle Method:

  19. x k -p/a p/a -a a Quantum mechanics Quiz 9c A particle is in a given initial state Y(x,0) what will be the shape of the Fourier transform F(k)? B. A. C. k k -p/a p/a

  20. Quantum mechanics Ch 2.4 where Dispersion relation here Physical interpretation: • velocity of the each wave at given k: • velocity of the wave packet: Free particle

More Related