Quantum Mechanics in a Nutshell Mr Finn April 2011

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!?

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

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”

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

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

Einstein’s Photons Classically light = wave –Light behaves like wave - interference –Maxwell predicted electricity & magnetism propagate through space as wave at speed of 3  10 8 m/s speed of light Shine light on metals - eject electrons –details inconsistent with waves –Einstein - light is particle or bundle of energy

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

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

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

Standing Waves

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? classical vs quantum probabilities flipping a coin?

Hydrogen orbitals

Heisenberg Uncertainty Quantities are “unknowable” –uncertainties inherent in nature Two uncertainty principles:

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, …

Feynman Diagram