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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 0 10 20 30 40 50 Score up to 0 2 4 6 8 10 12 # students
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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 = 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.
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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)
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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.
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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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