PHY 520 Introduction Christopher Crawford

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? 2

18 th century optimism: 3

But two clouds on the horizon… 4

5

… (wavy clouds) 6

The Extensions of Modern Physics 7

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 8

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

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

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=F  dx, momentum p=Fdt Wave equation – wave nature of light – Boundary Value Problems! 11

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 12

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 13

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 14