PHY 520 Introduction

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PHY 520Introduction

• Christopher Crawford
• 2015-08-26

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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?

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18th century optimism
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But two clouds on the horizon
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But two clouds on the horizon
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(wavy clouds)
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The Extensions of Modern Physics
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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

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Unification of 4 Fundamental Forces

• Where does Quantum Mechanics fit in?

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What is the essence of QM?

• Quantization (Planck)
• Correspondence (Bohr)
• Duality / Complementarity / Uncertainty
  (Heisenberg)
• Symmetry / Exclusion (Pauli)

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Dynamics of EM

• Maxwells equations dynamics of the field
• Source equations charge (?,J) generates field
• Force equations conservative nature of EM
  fieldsQ (current density), E (Poynting vector),
  p (stress tensor)
• Lorentz Force equation dynamics of particles
• Integrate to get energy EF?dx, momentum pFdt
• Wave equation wave nature of light
• Boundary Value Problems!

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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

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Mathematics from 416 -gt 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

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General course outline

• historical underpinnings
• Blackbody, photoelectric/Compton, Bohr model
• concepts
• quantization, correspondence, duality/complementar
  ity,
• 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