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Physics 451

Explore quantum mechanics concepts such as discrete and continuous variables, variance, normalization, and wave functions. Learn from notable scientists like Planck and Einstein. Dive into probability distributions and system probabilities.

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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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