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Understanding Quantum Mechanics: From Classical Probability to Modern Physics Applications

This agenda details key concepts from Chapters 6 and 7 of a physics course, focusing on the evolution of probability from classical to quantum mechanics. We will explore fundamental topics including quantum tunneling, the uncertainty principle, and Pauli's exclusion principle. The discussion also covers the implications of modern physics in fields such as medicine, quantum states, fermions, and bosons. The assignment of project ideas is due by Halloween, encouraging creative applications of these principles in contemporary science.

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Understanding Quantum Mechanics: From Classical Probability to Modern Physics Applications

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  1. Wednesday, October 17 Ford Chs: 6&7

  2. Agenda • Announce: • Read Chs. 8 & 9 • Project Ideas due by Halloween • Another project idea: Modern Physics in Modern Medicine • Ch. 6 • Ch. 7

  3. Probability Pre-Quantum • Physicists accepted probability even before quantum mechanics, but where? And how was it “different” from that in QM?

  4. Probability In QM • Can be computed precisely • All that one can compute…fundamentally limited in ability to predict (nondeterministic universe) • Mathematics describes a probability wave • Examples: • Jumps of electron to different states • Radioactive decays

  5. Radioactivity • Geiger counter makes activity at the level of the nucleus apparent! • Characterized by half-life • Wide range of half-lives • All unstable particles follow same exponential curve

  6. Nuclear Waste (spent fuel) • Lots of nasty radioactive material left over from nuclear reactors • Half-lives of years to hundreds of years • Can’t fix chemically • Essentially never safe • Need nuclear furnace (e.g. Sun, nuclear reactor)

  7. Quantum Tunneling • Object can pass through barriers which classically they could not

  8. Quantum Tunneling

  9. Uncertainty Principle • Fundamental limit to how well we can “know” certain pairs of quantities • The better you know one, the less well you know the other • E.g. position/momentum or energy/time • Already saw when trying to compress electrons…so knew where they were meant we knew little about momentum • Will see later on in the book (w/ waves)

  10. Is quantum probability real or just reflect our ignorance?

  11. Fermion/Boson • Fermions—half-odd-integer spin (e.g. electron, proton, neutron) • Bosons—integer spin (e.g. photon) • Very different behavior

  12. Quantum States • Particles can be in specific states • Such states have specific, quantized values for certain physical quantities (even if their motions are “fuzzy”) • Each state has certain quantum numbers (n,l,m)

  13. Pauli’s Exclusion Principle • No two fermions exist in the same state • No two fermions share the same quantum numbers • Predicted a fourth quantum number for the electron, spin • Responsible for chemistry, why?

  14. Bose-Einstein Condensate • Einstein predicted that bosons, at low enough temperature, would share the same state • Race in early 1990s to create one • Won by Wieman and Cornell in 1995 (shared in the 2001 Nobel Prize) • Practical applications? • Superfluidity • Atom lasers • superconductivity

  15. Keys to QM so far… • Interactions governed by? • Interactions & Jumps determined by? • Knowledge of these processes limited by?

  16. Keys to QM so far… • Interactions governed by? • Fundamental particles • Absorbing and emitting force carriers • Following certain conservation laws • Interactions & Jumps determined by? • probabilities • Knowledge of these processes limited by? • Uncertainty principle

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