l12 - A few things Quantum mechanics Schrödinger’s cat...

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Unformatted text preview: A few things Quantum mechanics Schrödinger’s cat Slit example Schrödinger cookbook Infinite quantum well Infinite box: 2D Harmonic oscillator Motion at zero temperature A few things • Regarding HW5 problem 6 (Serway 4.38), I led some people astray. Conservation of energy says K = ( K − Δ K ) + K M or K M = Δ K . I had said let K M be zero which is wrong! Suggestion: write conservation of momentum and energy equations in terms of v , v ′ , and V for electron before, electron after, and mercury after. Also define x ≡ M / m e . Calculate 1 2 m e v 2 − 1 2 m e v ′ 2 = Δ K . • Grades: last semester the A/B threshold was somewhere in the neighborhood of low 80%, and the B/C threshold was in the mid 60% range. As they say with mutual fund advertisements: past performance is not a prediction of future results . . . Phy251, Fall 2009, Exam 1 10 20 30 40 50 Score up to 2 4 6 8 10 12 # students A few things Quantum mechanics Schrödinger’s cat Slit example Schrödinger cookbook Infinite quantum well Infinite box: 2D Harmonic oscillator Motion at zero temperature Schrödinger equation • From using k = 2 pi /λ , λ = h / p , p 2 / 2 m = K , and E = K + U or kinetic plus potential energy, Schrödinger arrived at an equation for matter waves in a non-time-varying potential energy landscape U : − planckover2pi1 2 2 m ∂ 2 ∂ x 2 ψ + U ψ = E ψ • When the potential energy landscape also varies with time, the time-dependent version is found using E = planckover2pi1 ω as − planckover2pi1 2 2 m ∂ 2 ∂ x 2 ψ + U ψ = − i planckover2pi1 ∂ ∂ t ψ. A few things Quantum mechanics Schrödinger’s cat Slit example Schrödinger cookbook Infinite quantum well Infinite box: 2D Harmonic oscillator Motion at zero temperature Born/Copenhagen interpretation • See Serway Sec. 6.1. The most commonly accepted interpretation of Schrödinger’s equation arose from the work of Max Born, and also discussions in Niels Bohr’s institute in Copenhagen. • Matter waves ψ describe not the particle, but its probability amplitude. • ψ † ψ = | ψ | 2 represents the probability. Therefore we realize that integraltext | ψ | 2 should be normalized to 1. Max Born (1882– 1970; Nobel Prize 1954) A few things Quantum mechanics Schrödinger’s cat Slit example Schrödinger cookbook Infinite quantum well Infinite box: 2D Harmonic oscillator Motion at zero temperature What’s waving? Electron waves! 8 quanta 270 2,000 60,000 From A. Tonomura, Electron Holography (Springer-Verlag, 1993), p. 14. A few things Quantum mechanics Schrödinger’s cat Slit example Schrödinger cookbook Infinite quantum well Infinite box: 2D Harmonic oscillator Motion at zero temperature Light and matter Property Light QM Amplitude ψ = Ae − i ( kx − ω t ) Electric field E = ψ Probability amplitude ψ Amplitude squared | ψ | 2 = ψ † ψ Electric field squared gives irradiance (from the Poynt- ing vector in classical E&M): I = radicalbig ǫ/μ ( E ) 2 ....
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This note was uploaded on 05/28/2011 for the course PHY 251 taught by Professor Rijssenbeek during the Fall '01 term at SUNY Stony Brook.

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l12 - A few things Quantum mechanics Schrödinger’s cat...

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