PHY 520 Introduction Christopher Crawford 2015-08-26.

PHY 520IntroductionChristopher 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– 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 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 energy E=Fdx, momentum p=Fdt

• 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 -> 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/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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