1. Christopher Crawford 2017-08-23
PHY 520 Introduction
Christopher Crawford

2. Course mechanics Introductions / class list Canvas / course webpage
Syllabus

3. What is physics? Study of … 4 pillars of physics:
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?

4. 18th century optimism:

5. But two clouds on the horizon…

6. But two clouds on the horizon…

7. … (wavy clouds)

8. Modern Revolution
October 1927 Fifth Solvay International Conference on Electrons and Photons

9. The Extensions of Modern Physics

10. Key principles of QM Quantization (Planck, Einstein, deBroglie)
Waves are quantized as packets of energy (particles)
Particles have quantized energy from modes of their wave functions.
Correspondence (Bohr)
Agreement with classical mechanics for large quantum numbers
Duality / Complementarity / Uncertainty (Heisenberg)
Complementary variables cannot be simultaneously measured
Symmetry / Exclusion (Pauli)
Identical particles cannot be distinguished-> symmetric wavefunction

11. State and Equation of Motion
Classical mechanics
The initial state of a particle is it’s position x0 and velocity v0
The equation of motion is Newton’s 2nd law: F=m d2x/dt2
Integrate this ODE with initial conditions to determine trajectory x(t)
In principle, exact position, velocity known at all times
Conservation: it is usually easier to work energy & momentum
Quantum mechanics
The initial state of a particle is it’s initial wave function 0 (x)
Equation of motion: TDSE: –ħ2/2m d2/dx2 + V(x)  = iħ d/dt
Solve this PDE boundary value problem to evolve (x,t) in time
A measurement of position yields a random value according to the probability distribution |(x,t)|2dx
Measurement “collapses the wavefunction” so that a subsequent measurement is certain to yield the same value

12. General course outline
Ch. 1+: Historical underpinnings -> TDSE & wave function
Blackbody radiation, de Broglie mater waves, Bohr model
Quantization and dispersion: propagation of wave functions (TDSE)
Complementarity and the uncertainty principle
Ch. 2: Solutions of the time-independent Schrödinger Eq.
Infinite square well, harmonic oscillator, free particle, delta function
Finite square well: bound/unbound states; transmission/ reflection
Ch. 3: Formalism of Quantum Mechanics
Mathematical review; Dirac bra-ket formalism
Hilbert space, operators(observables), eigenfunctions
Postulates of Quantum Mechanics
Ch. 4: 3-d systems
Angular momentum, hydrogen atom

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