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Quantum Theory 3

Quantum Theory 3. Topics. Wave-Particle Duality The Schrödinger Equation Interpretation of Wavefunction Summary. Wave-Particle Duality. In 1905, Einstein interpreted Planck’s quantum as a particle of light, now called a photon , and showed how the photon concept yields a simple

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Quantum Theory 3

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  1. Quantum Theory 3

  2. Topics • Wave-Particle Duality • The Schrödinger Equation • Interpretation of Wavefunction • Summary

  3. Wave-Particle Duality In 1905, Einstein interpreted Planck’s quantum as a particle of light, now called a photon, and showed how the photon concept yields a simple explanation of the photoelectric effect Light, therefore, has a dual nature: it sometimes manifests wave properties and sometimes particle properties

  4. Wave-Particle Duality In 1924, Prince Louis de Broglie proposed that the duality is a general aspect of Nature 1892 – 1987

  5. Wave-Particle Duality Louis de Broglie, proposed the following as general laws of Nature: The de Broglie Relations 1892 – 1987

  6. Wave-Particle Duality de Broglie showed that Bohr’s quantization condition for angular momentum is equivalent to the condition if electrons are “wave-like” entities

  7. Wave-Particle Duality In 1927, C. Davisson and L. Germer confirmed that electrons can be diffracted in exactly the same way as light, thereby confirming de Broglie’s hypothesis Proceedings of the National Academy of Sciences, 14, 619 (1928)

  8. (b) Diffraction by x-rays with λ = 0.07 nm (c) Diffraction by electrons with λ = 0.05 nm

  9. The Schrödinger Equation • In late 1925, building on • de Broglie’s idea, • Erwin Schrödinger • proposed the • following wave equation ħ = h/2p 1887 – 1961 1887 – 1961 is a complex number called the wavefunction

  10. x x + dx p(x) x Interpretation of Wavefunction p(x)dx is the probability to find a particle between x and x + dx Max Born 1882 – 1970

  11. The Double Slit Experiment http://www.hitachi.com/rd/research/em/doubleslit.html

  12. The Uncertainty Principle In 1925, Heisenberg proposed the first version of quantum theory. Two years later he formulated the uncertainty principle 1901 – 1976

  13. Minimum Energy of a Particle in a Box Consider a 1-d “box” Since the particle can be anywhere in the box, Δx = L, so L But and the average kinetic energy is assuming speeds very much less than c zero point energy

  14. But What is it, Particle or Wave? Consider the experiment below If a photon is a particle, then each one will be detected either at A or B and never at both A and B A 1 1 This is the behavior expected of a particle: the particle goes along either path 1 or 2 Single photon source 2 B half-silvered mirror

  15. But What is it, Particle or Wave? Now replace the detectors at A and B by mirrors C D A 1 If the photon is a particle, it should be detected either at C or D with equal chance But quantum theory predicts the photon will be detected always at D, or always at C! 1 2 Single photon source 2 B half-silvered mirror

  16. Summary • Quantum Theory • The Schrödinger equation describes quantum objects in terms of a complex number Ψcalled a wavefunction • |Ψ|2is interpreted as the probability density to find the object in a given region • Uncertainty Principle • Δx Δp ≥ h/2π • Quantum objects are neither particles nor waves! • They are like nothing in our everyday experience

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