Phy107Spr07Lect28 - Classical vs quantum From Last Time A...

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1 Fri. Mar. 30, 2007 Phy107 Lect 28 1 From Last Time… Atoms: quantized orbits quantized energies quantum states labeled by integers n=1,2,3… Atomic spectra: photon emission and absorption Fri. Mar. 30, 2007 Phy107 Lect 28 2 Classical vs quantum Low classical amplitude, low energy Higher classical amplitude, higher energy Fri. Mar. 30, 2007 Phy107 Lect 28 3 Probability density of oscillator Moves fast here, low prob of finding in a ‘blind’ measurement Moves slow here, high prob of finding Classical prob Fri. Mar. 30, 2007 Phy107 Lect 28 4 Zero-point energy • In all cases, wave represents the quantum- mechanical nature of the particle. • In all cases, the lowest energy state represented a particle with some motion. • The particle can NEVER sit still. • This also comes from the uncertainty principle – If the particle were sitting still, it’s momentum would be accurately zero. – Means that position is completely uncertain. Fri. Mar. 30, 2007 Phy107 Lect 28 5 Unusual wave effects Classically, pendulum with particular energy never swings beyond maximum point. This region is ‘classically forbidden’ Quantum wave function extends into classically forbidden region. Classically forbidden region End of swing Fri. Mar. 30, 2007 Phy107 Lect 28 6 • Quantum mechanics predicts some probability of the pendulum being found beyond the limits of it’s swing! • This is a common effect in quantum mechanics, arising from wave nature of particle.
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2 Fri. Mar. 30, 2007 Phy107 Lect 28 7 Particle in a box, again L Wavefunction Probability = (Wavefunction) 2 Particle contained entirely within closed tube. Open top: particle can escape if we shake hard enough. But at low energies, particle stays entirely within box. Like an electron in metal
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Phy107Spr07Lect28 - Classical vs quantum From Last Time A...

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