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SJ_MB_QMnotes - 3D ∇ − = i p 1D dx d i p x − =...

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Plan of action: - Background; - “Postulates” of QM; - Application #1: Particle in a Box Application #2: Atomic orbitals; Hints leading to QM: - Discrete spectral lines; - Specific heats of solids (Law of Dulong and Petit, 3R); - Photoelectric effect; - Davisson-Gerner experiment (electron diffraction); Theoretical Responses: - Discrete spectral lines: Niels Bohr 2 2 4 2 2 1 2 6 . 13 n h me eV n E n π = = ; - De Broglie: “pilot waves” Attribute a wavelength to matter: p h = λ ; Classical Mechanics Quantum Mechanics 1) The “state” of a system { } i i p q , “wave function” ) ( x ψ 2) Evolution Equations i i q H p = ; i i p H q = ψ ψ H t i ˆ = 3) Observables and measurements Any mechanical variable we might be interested in is a function of p’s and q’s, e.g. 2 2 2 1 2 kq m p E + = i) dx x 2 ) ( ψ probability that particle will be found between x and x+dx ii) “Expected” value of an observable, C ˆ , is given by C x C ˆ ) ( ˆ * ψ ψ ψ ψ = Question: What observables?
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