Quantum Mechanics in a Nutshell

1. Quantum Mechanics in a Nutshell Mr Finn April 2011

2. S. James Gates • How can there be two separate everywheres? • one everywhere = atoms governed by quantum mechanics • another everywhere = galaxies governed by general relativity … but galaxies are comprised of atoms!?

3. Atoms • Democritus • “atom” = indivisible • Dalton • All matter comprised of small indivisible particles. • All atoms of given element are identical. • Compounds are comprised of two or more atoms in definite ratios of small whole numbers. • Atoms are neither created nor destroyed in chemical reactions; they are rearranged. Atoms have no internal parts

4. J.J. Thomson • Electrons • cathode rays: vacuum tube with high voltage • very light, negative particles • piece of atom (?) • Model of atom • negative electrons • positive “gel”

5. Ernst Rutherford • Discovery of nucleus • shot positive particles through Thomson’s atoms • should pass through but slowed • but ricocheted backwards or passed through unaffected • model • atoms - positively charged core = nucleus • empty space = orbiting electrons

6. Atomic Spectra • Light emitted by elements • discrete “special” colors • inconsistent with planetary model • Unique for each element

7. Einstein’s Photons • Classically light = wave • Light behaves like wave - interference • Maxwell • predicted electricity & magnetism propagate through space as wave at speed of 3108 m/s • speed of light • Shine light on metals - eject electrons • details inconsistent with waves • Einstein - light is particle or bundle of energy

8. Shoot a single at stone wall and something will be ejected, regardless of the number of bullets. Analogy Ping pong ball = Low energy photon, below cut-off Bullet = high energy photon, above cut-off Shoot ping pong balls at stone wall and nothing ejected. Increasing the intensity = more ping pong balls  no effect.

9. Bohr Atomic Model • Proposed “special orbitals” • Electron cannot orbit at any distance, only “special” ones • light emit/absorb as electrons “jump” between “special” orbits • no justification (?) • except matches atomic spectra

10. de Broglie Model • Light = wave and particle properties • Matter = ditto (!?) • electrons seen to behave like waves and create interference patterns • Atoms • electrons are standing waves • wavelength  circumference of Bohr special orbitals

11. Standing Waves

12. Schrödinger Model • Wave equation for hydrogen atom • solution ()= complex number, standing wave • no obvious meaning (!?) • convert to real number (*) • wave function value between 0 and 1 • probability of finding electron • electron - no classical trajectory • only compute probabilities classical vs quantum probabilities flipping a coin?

13. Heisenberg Uncertainty • Quantities are “unknowable” • uncertainties inherent in nature • Two uncertainty principles:

14. Quantum Field Theory • Force = exchange of particle • each force has a particle that “carries” force • electromagnetic force  photon • weak nuclear force  “vector boson” • strong nuclear force  gluon • Feynman Diagrams • weak force: convert n  p • strong: binds quark, n/p • quarks: make up n, p, …