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Physics 451

Physics 451. Quantum mechanics I Fall 2012. Karine Chesnel. Homework. Homework 1: Today Aug 31 st by 7pm Pb 1.1, 1.2, 1.3 Homework 2: Group presentations Sep 5th Homework 3: F Sep 7th by 7pm Pb 1.4, 1.5, 1.7, 1.8. Phys 451. Announcements.

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Physics 451

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  1. Physics 451 Quantum mechanics I Fall 2012 Karine Chesnel

  2. Homework • Homework 1: Today Aug 31stby 7pm • Pb 1.1, 1.2, 1.3 • Homework 2: Group presentations Sep 5th • Homework 3: F Sep 7th by 7pm • Pb 1.4, 1.5, 1.7, 1.8 Phys 451 Announcements Monday Sep 3: NO CLASS (Holiday) Help sessions: T Th 3-6pm

  3. Phys 451 Announcements Next class Sep 5th Group presentations Will count as homework 2, 20 pointsplus 5 quiz points for presenting Famous scientist who contributed to the foundation of Quantum Mechanics Planck De Broglie Einstein Schrödinger Born Bohr Heisenberg Dirac Pauli

  4. Distribution of scores in a class Age pyramid for a certain population (Utah, 2000) Quantum mechanics Probabilities Discrete variables Examples of discrete distributions:

  5. Example: number of siblings for each student in the class Distribution of the system Probability for a given j: Average value of j: Average value of a function of j Average value “Expectation” value Quantum mechanics Probabilities Discrete variables

  6. Quantum mechanics Quiz 2a What is the definition of the variance? A. B. C. D. E.

  7. The deviation: The standard deviation Quantum mechanics Probabilities Discrete variables Variance

  8. intensity brightness Spectral analysis of a photograph Wide: large s Narrow: small s Quantum mechanics Probabilities Discrete variables The variance defines how wide/narrow a distribution is Distribution of scores in a class

  9. The density of probability: Probability to find the particle between positions a and b: Normalization: Quantum mechanics Probabilities Continuous variables The probability of finding the particle in the segment dx

  10. Variance: Quantum mechanics Probabilities Continuous variables Average values:

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

  12. Quantum mechanics Quiz 2b Is this wave function square integrable or not? A. YES B. NO

  13. Normalization: If Y satisfies the Schrödinger equation and is normalizable, then indeed Quantum mechanics Normalization of Wave function Can Y stay normalized in time?

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