l11 - Review Quantum Mechanics Heisenberg Schrödinger...

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Unformatted text preview: Review Quantum Mechanics Heisenberg Schrödinger What’s waving? Infinite quantum well Born/Copenhagen interpretation Schrödinger’s cat The Bohr model • Thomson and Millikan: discovery of the electron, its ratio q / m , and then its charge q . “Classical” radius: r e = 2 . 82 × 10- 15 m. • Rutherford: all of an atom’s positive charge is in a very small nucleus, with r ≃ 10- 14 m. • Bohr model (1913): • Rearrange centripetal=electrostatic force to find constants at atomic length scale, in expression with angular momentum. • Angular momentum ℓ is in units of Planck’s constant h . • Postulate ℓ = n planckover2pi1 with planckover2pi1 = h / 2 π . • Fantastic agreement with hydrogen spectra, and good agreement with Moseley’s law and the Franck-Hertz experiment! r = n 2 Z a with a = . 053 nm (1) E =- Z 2 n 2 E with E = 13 . 60 eV (2) Review Quantum Mechanics Heisenberg Schrödinger What’s waving? Infinite quantum well Born/Copenhagen interpretation Schrödinger’s cat Bohr model: problems • The Bohr model is fantastically successful predicting the energies of 1-electron atoms and ions! • It becomes less and less accurate when you take into account more and more electrons. • Bohr and others extend it: parabolic orbits, etc . . . But still not fully successful. • By the mid-1920s, it is clear that while the Bohr model provides important insights, it is not complete and fully correct. • The meaning of the Bohr model is also mysterious. Why is it that ℓ = n planckover2pi1 ? • In 1924, Louis de Broglie provides an explanation: λ = h / p , so ℓ = n planckover2pi1 describes standing waves. • Wavelike nature of matter confirmed by Davisson and Germer in 1927. Review Quantum Mechanics Heisenberg Schrödinger What’s waving? Infinite quantum well Born/Copenhagen interpretation Schrödinger’s cat Quantum Mechanics It all began when Volkswagen introduced the Quantum in the US market in 1982. Somebody needed to repair the things! Here’s one that was for sale on EBay that really needed a Quantum mechanic: Review Quantum Mechanics Heisenberg Schrödinger What’s waving? Infinite quantum well Born/Copenhagen interpretation Schrödinger’s cat Well . . . the real birth of quantum mechanics Max Born, “Quantum mechanics,” Zs. f Phys. 26 , 379–395 (1924); paper received June 13: This paper contains an attempt to make a first step towards a quantum theory of cou- pling, which takes into account some of the more important properties of atoms (sta- bility, resonance for transition frequencies, correspondence principle) and which also arises in a natural way from the classical laws . . . What we shall do is to bring the classical laws for the perturburation of a mechanical system, caused by internal cou- plings or external fields, into one and the same form, which would very strongly sug- gest the formal passage from classical me- chanics to ‘quantum mechanics.’ Max Born (1882–1970; Nobel Prize 1954) Review...
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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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l11 - Review Quantum Mechanics Heisenberg Schrödinger...

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