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StudyGoals_for_Students

# StudyGoals_for_Students - Here were some Chapter by Chapter...

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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 "Ψ" tells you: you should know how to use it to figure out probability of measurement. Do you know the difference between probability and probability density? Can you compute expectation values or standard deviations, given information about either discrete or continuous probabilities? Operators : You should be able to interpret and calculate expectation values of any (position space) operator using the position-space wave function "ψ(x)". Specifically, you should know the "operator form" of momentum (p = ħ/i d/dx) You should know the connection <p> = m d<x>/dt, and be able to work through calculations like the one proving "conservation of normalization" using the Schrödinger equation. Heisenberg relations : You should have a preliminary sense of the uncertainty principle (be able to state it, and physically interpret the two "sigma" terms, as well as calculating them given a state) We spent some time talking about the Postulates of quantum mechanics, the motivation for the Schrödinger equation (including deBroglie's very important idea, the p = ħ /λ or p = ħ k story), and a little history - you should be familiar with these. _______________________ Chapter 2: Schrödinger Equation: The relation between the time DEpendent Schrödinger equation, and the time INdependent SE is quite central here - you should know the "separation of variables" trick, and thus be able to go from u n (stationary states, i.e. , solutions of H u = Eu, the TISE) to more general states (with proper time dependence.) Stationary States and Expectation Values: You should have a clear idea of our definition of "stationary state", how you find one (at least, for the specific examples of infinite square well and harmonic oscillator), what they "look like" (graphs), what their time dependence is, and be able to compute (and qualitatively explain or predict) what expectation values look like (<x>, <p>, <H>, <x 2 >, etc. ) Expansion in Stationary States: You should also understand how a more GENERAL

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StudyGoals_for_Students - Here were some Chapter by Chapter...

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