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Quantum Mechanics The predictions of quantum mechanics are rather bizarre from classical point of view: Propositions of classical physics: 1. The physical universe is deterministic, i.e., given enough information about a physical system, its future evolution can be predicted exactly. The entire function of classical mechanics is to derive such predictions. 2. Light consists of waves, which ordinary matter is composed of particles. The former statement is one of the triumphs of classical electromagnetism, while the latter seems self-evident. 3. Physical quantities, such as energy and angular momentum, can be treated as continuous variables, Again, this assumption is built into the structure of classical mechanics. 4. There exists an objective physical reality independent of any observer. If tree falls in the woods, of course it makes a sound. Propositions of Quantum Mechanics: 1. The physical universe is not deterministic. At the subatomic level, we can assign probabilities to the outcome of certain experiments but never predict the exact result with certainty. Uncertainty is an intrinsic property of matter at this level. 2. Both light and matter exhibit behavior that seems characteristic of both particles and waves. 3. Under certain circumstances, some physical quantities are quantized, i.e., they can take on only certain discrete values. 4. Finally, it appears that the observer always affects the experiment; it is impossible to disentangle the two. Why would anyone believe such a preposterous set of ideas? For the only reason that any theory in physics is given credence: because it works!!! What is quantum mechanics? Quantum mechanics is a quantum theory that supersedes classical mechanics at the atomic and subatomic levels. It is a fundamental branch of physics that provides the underlying mathematical framework for many fields of physics and chemistry, including condensed matter physics, atomic physics, molecular physics, computational chemistry, quantum chemistry, particle physics, and nuclear physics. It is a pillar of modern physics, together with general relativity. Electron waves imaged by STM You see electron waves!! Quantum Corral Writing with atoms Lecture 1 The emergence of quantum mechanics Best historical review: 3 Hans Bethe’s lectures: http://bethe.cornell.edu/ 1.1 Collapse of Classical Physics • Wave-particle duality • Stability of atoms 1.2 Historical view on the emergence of quantum physics 1911 Solvay Conference Seated (L-R): W. Nernst, M. Brillouin, E. Solvay, H. Lorentz, E. Warburg, J. Perrin, W. Wien, M. Curie, and H. Poincaré. Standing (L-R): R. Goldschmidt, M. Planck, H. Rubens, A. Sommerfeld, F. Lindemann, M. de Broglie, M. Knudsen, F. Hasenöhrl, G. Hostelet, E. Herzen, J.H. Jeans, E. Rutherford, H. Kamerlingh Onnes, A. Einstein, and P. Langevin. 1927 Solvay Conference Seated (L-R): Walther Nernst, Marcel Brillouin, Ernest Solvay, Hendrik Lorentz, Emil Warburg, Jean Baptiste Perrin, Wilhelm Wien, Marie Curie, and Henri Poincaré. Standing (L-R): Robert Goldschmidt, Max Planck, Heinrich Rubens, Arnold Sommerfeld, Frederick Lindemann, Maurice de Broglie, Martin Knudsen, Friedrich Hasenöhrl, Georges Hostelet, Edouard Herzen, James Hopwood Jeans, Ernest Rutherford, Heike Kamerlingh Onnes, Albert Einstein, and Paul Langevin. 1.3 The birth of photon: photoelectric effect E v ? Metal surface hνth = Φ What are not understood by classical mechanics? • • v Threshold frequency E does not depend on light intensity but depend on frequency A minimum frequency (not intensity) is required for the photoelectron emission Einstein hypothesized that light is composed of localized bundles of electromagnetic energy called photon (hν) E = hν - Φ Sommerfeld Fermi gas model E hν Vacuum level EF Φ (work function) Fermi sea of electrons Electrons are excited by quanta of light instead of classical electromagnetic wave ! 1.4 Compton scattering Arthur H. Compton observed the scattering of x-rays from electrons in a carbon target and found scattered x-rays with a longer wavelength than those incident upon the target. The shift of the wavelength increased with scattering angle. Compton explained and modeled the data by assuming a particle (photon) nature for light and applying conservation of energy and conservation of momentum to the collision between the photon and the electron. Photon: (hc/λi, Pi) → (hc/ λf, Pf) Electron: (mec2, 0) → (√[pec2 + (mec2)2], pe) Compton formula Another direct proof of quantization of light: photon 1.5 Blackbody radiation: birth of Planck constant Any theory based on continuous radiation of electromagnetic waves failed to reproduce the observed curves Planck assumed that the energy radiated from radiation oscillators could be only some whole number multiple of hν where is the planck constant: ε = nhv, n = 1,2,3, … Radiation energy density: the energy per unit volume per unit frequency Application of Planck formula Background radiation (2.7K) of the universe 1.6 DeBroglie hypothesis and Devisson-Germer experiment Why Bohr’s orbitals of atoms are quantized? (L = mvrn = n= ) Photon case: p = E/c = hν/c = hλ ω = 2πν λ = h/p k = 2π/ λ p = =k where = = h/(2π) deBroglie Hypothesis: Any particle moving with a momentum p would have a wave of matter with its wavelength as λ = h/p For an electron in an atom, the stationary orbits in the Bohr model has an integral number of wavelengths. 2πrn = nλ This experiment demonstrated the wave nature of the electron, confirming the earlier hypothesis of deBroglie. Putting wave-particle duality on a firm experimental footing, it represented a major step forward in the development of quantum mechanics. Low energy electron diffraction: d sinθ = n λ Wave-particle duality: matter exhibits properties of both waves and particles. 1.7 Heisenberg Uncertainty Principle The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa. --Heisenberg, uncertainty paper, 1927 One cannot measure values (with arbitrary precision) of certain conjugate quantities, which are pairs of observables of a single elementary particle. These pairs include the position and momentum sinθ ~ θ m=1 λ = h/p ~ h/px ∆y ~ a ∆py/px ~ θ a sin θ = λ ∆y ∆py/px ~ h/px ∆y ∆py ~ h 1.8 References and homework • • • • R.l. Liboff, Introductory Quantum Mechanism http://bethe.cornell.edu/ http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html http://en.wikipedia.org/wiki/Quantum_mechanics