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Physics 451

Physics 451. Quantum mechanics I Fall 2012. Sep 7, 2012 Karine Chesnel. Homework. Homework 3: F Sep 7th by 7pm Pb 1.4, 1.5, 1.7, 1.8 Homework 4: T Sep 11 by 7pm Pb 1.9, 1.14, 2.1, 2.2 Homework 5: Th Sep 13 by 7pm Pb 2.4, 2.5, 2.7, 2.8. Phys 451. Announcements.

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Physics 451

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  1. Physics 451 Quantum mechanics I Fall 2012 Sep 7, 2012 Karine Chesnel

  2. Homework • Homework 3: F Sep 7th by 7pm • Pb 1.4, 1.5, 1.7, 1.8 • Homework 4: T Sep 11 by 7pm • Pb 1.9, 1.14, 2.1, 2.2 • Homework 5: Th Sep 13 by 7pm • Pb 2.4, 2.5, 2.7, 2.8 Phys 451 Announcements Please don’t forget to submit your homework on time! Help sessions: T Th 3-6pm

  3. Phys 451 Remarks from the TA after grading the first homework • Simplify your answers to their simplest forms. • Don't leave it like x=(1/3-1/5)^(1/2) or x=1-Sigma, • while you already have a value for Sigma. • 2. Don't make your "rough sketch" too rough. Label your axes, and draw • the curve nicely. Be a little more professional than the Physics 121 students. • 3. Some simple calculus and graphs can be done by hand, • such as a standard Gaussian. Don't rely entirely on Mathematica. • 4. Don't write too compactly. Leaving enough space in your writing not • only benefits the TA but also helps yourself when you go back and check. • 5. Write your CID instead of your name.

  4. Quantum mechanics Quiz 3a Evolution of Y in time? “If the wave function is normalized at a time t, it is then normalized at any time.” A. True B. False

  5. Density of probability (now function of space and time): Normalization: Solutions have to be normalizable: - needs to be square-integrable Quantum mechanics Probabilities & Wave function

  6. Density of probability: Average position x: Average value for f(x): Quantum mechanics Expectation values Probabilities Quantum Mec.

  7. Differentiation between expectation value and most probable value See pb 1.4 and pb 1.5 Quantum mechanics Expectation values The expectation value is the average of all the measurements of the quantity f on a ensemble of identically prepared particles

  8. Schroedinger equation Expectation value for the velocity Expectation value for the momentum Quantum mechanics Expectation values Evolution of <x> in time?

  9. “Operator” x “Operator” p Quantum mechanics Expectation values Generalization

  10. Kinetic energy: • Angular momentum: Quantum mechanics Expectation values Examples and so on..

  11. Equivalent to Newton’s second law Quantum mechanics Ehrenfest’s theorem See pb 1.7

  12. ? (picking an extra phase) Y ? (no effect) Quantum mechanics Effect of potential offset? V+V0 V See pb 1.8

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