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02_580_syllabus - Physics 580 Handout 2 24 August 2010...

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Physics 580 Handout 2 24 August 2010 Quantum Mechanics I webusers.physics.illinois.edu/ goldbart/ Prof. P. M. Goldbart 3135 (& 2115) ESB University of Illinois Classical mechanics : principal of least action; lagrangian mechanics, symmetries and conservation laws; hamiltonian mechanics, Poisson brackets and canonical transformations; charged particle mechanics. Mathematical scaffolding for quantum mechanics : linear vector spaces, Dirac nota- tion, linear operators; hermitean operators; eigenvalue problems and functions of operators; spaces of infinite dimension; self-adjoint operators; the Dirac delta function and Fourier transforms. Some interesting experiments : the photo-electric effect; Taylor’s two-slit experiment; Davisson-Germer experiment; Franck-Hertz experiment; Stern-Gerlach experiment. Wave mechanics : the time-dependent Schr¨odinger equation; probability densities and cur- rents. The postulates of quantum mechanics : the postulates and their meaning; state vectors
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