phys3313-lec10 - Physics 3313 - Lecture 10 Monday September...

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Physics 3313 - Lecture 10 9/28/2009 1 3313 Andrew Brandt Monday September 28, 2009 Dr. Andrew Brandt 1. HW4 due Weds Sep. 30, test on Ch 1-5 Oct. 14 2. Schrodinger’s Equation 3. Wave Function Properties 4. Operators and Expectation Values 5. Eigenfunctions and Eigenvectors
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Quantum Mechanics Bohr theory: -Successful for Hydrogen and one electron atoms -Does not explain some subtle aspects of spectral lines -Does not predict how atoms interact New theory of Quantum Mechanics (QM) needed QM makes predictions (often surprising) of remarkable accuracy Modern physics is based on QM QM deals with probabilities: the Bohr radius is most probable value of electron distance from nucleus, not exact value Classical mechanics, given initial conditions, momenta, and forces is deterministic, but due to uncertainty principle, QM is not is wave function of an object while is the probability of finding an object at a given place and time QM can be used to determine the wave function under the influence of external forces, and the wave function can then be used to obtain the momentum, angular momentum, and energy 9/23/2009 3313 Andrew Brandt 2 (, ,,) xyzt Ψ 2 Ψ
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QM Wave Equation Recall general traveling wave solution: In QM, wave function Ψ may be complex (unlike y), so generalize to where With and we obtain This represents a particle with energy E and momentum p moving freely in the positive x direction Interested in motion of particle when acted upon by forces This requires a fundamental differential equation (Schrodinger’s Equation) which cannot be rigorously derived Let’s do years of work in a couple of bullet points! 9/23/2009 3313 Andrew Brandt 3 cos( ) y A t kx ω = ( ) i t kx Ae −− Ψ= cos sin i ei θ θθ = E hv = = 2 2 h pk π πλ = = ( ) ( ) / , i Et px x t Ae
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Aside on Partial Derivatives How do I take the derivative of when both x and y are variables? Partial derivative holds one variable as fixed while one takes the derivative with respect to the other variable.
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phys3313-lec10 - Physics 3313 - Lecture 10 Monday September...

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