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PHY 520 Introduction

PHY 520 Introduction. Christopher Crawford 2015-08-26. What is physics?. Study of … Matter and interactions Symmetry and conservation principles 4 pillars of physics: Classical mechanics – Electrodynamics Statistical mechanics – Quantum mechanics Classical vs. modern physics

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PHY 520 Introduction

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  1. PHY 520Introduction Christopher Crawford 2015-08-26

  2. What is physics? • Study of … • Matter and interactions • Symmetry and conservation principles • 4 pillars of physics: • Classical mechanics – Electrodynamics • Statistical mechanics – Quantum mechanics • Classical vs. modern physics • What is the difference and why is it called classical?

  3. 18th century optimism:

  4. But two clouds on the horizon…

  5. But two clouds on the horizon…

  6. … (wavy clouds)

  7. The Extensions of Modern Physics

  8. Classical Field vs Quantum Mechanics? • action at a distance vs. locality • field ”mediates “carries force • extends to quantum field theories • field is everywhere always E (x, t) • differentiable, integrable • field lines, equipotentials • PDE – boundary value problems • solution to physical problems

  9. Unification of 4 Fundamental Forces • Where does Quantum Mechanics fit in?

  10. What is the essence of QM? • Quantization (Planck) • Correspondence (Bohr) • Duality / Complementarity / Uncertainty (Heisenberg) • Symmetry / Exclusion (Pauli)

  11. Dynamics of E&M • Maxwell’s equations – dynamics of the field • Source equations – charge(ρ,J)generates field • Force equations –conservative nature of E&M fields:Q (current density), E (Poynting vector), p(stress tensor) • Lorentz Force equation – dynamics of particles • Integrate to get energyE=Fdx, momentump=Fdt • Wave equation – wave nature of light • Boundary Value Problems!

  12. Dynamics of Quantum Mechanics • Postulates [Sudbery]: • I. Principle of superposition • II. Results of experiments • III. Projection postulate / transition probabilities • IV. Position and momentum of a particle • V. Combined systems • VI. Undisturbed time development • VII. Translations and rotations • Mechanics • State vector records all we know about it • Schrodinger equation governs time evolution of state • Projection postulate governs interactions / measurements

  13. Mathematics from 416 -> 520 • Probability distributions • weighted average (expectation) • Fourier decomposition • Wave particle duality • General linear spaces • Vectors, functional, inner product, operators • Eigenvectors • Sturm-Louisville, Hermitian operators • Symmetries • Transformations, Unitary operators

  14. General course outline • historical underpinnings • Blackbody, photoelectric/Compton, Bohr model • concepts • quantization, correspondence, duality/complementarity, • Uncertainty principle, exclusion principle • postulates [Hilbert space] • state vector, observable operator, wave propagation, particle interaction • representations • wave mechanics (continuous) • matrix mechanics (discrete) • applications • various 1,2,3-D potentials; angular momentum; Hydrogen atom

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