Quantum Superposition Mark Van Raamsdonk

The Quantum World All matter made of elementary particles Modern physics: understand in detail how nature works at distances 100,000,000,000,000 times smaller than we can see!

Classical physics fails at these distance scales

Orbiting charge would produce EM radiation This carries away energy Electron losing energy spirals into nucleus Atoms would be unstable by classical rules All atoms would cease to exist in a nanosecond

The double slit experiment Bright line appears directly between the slits, with other bright lines to the sides

Explain via wave interference Recall: light is a wave of oscillating electric and magnetic fields Oscillating electric field Oscillating magnetic field James Clerk Maxwell 1864

Light waves from two slits add up to make bright central line Constructive Interference In this direction, light from two slits is “out of phase” and cancels Destructive Interference

CRUCIAL POINT: Pattern on screen results from combination of light waves from the two different slits.

Surprise: same result for electrons XXXX ELECTRON XXXX more electrons less electrons Electrons behave like waves?? Interference between different electrons going through the two slits?? (No!)

Bigger surprise: same pattern when we send in one at a time! Each electron can “see” both slits!

Explanation: quantum superposition electrons can be in two places at once! Electron at a definite location Single electron at a superposition of two locations Single electron at a superposition of many locations Electron in superposition has no definite location until we measure it

The wavefunction Mathematically, we describe a quantum superposition by a function  x)  is larger/smaller in magnitude in places where we are more/less likely to find electron  largest here  zero here

Schrodinger’s Equation Determines how wavefunctions will evolve with time Correctly explains double slit experiment in terms of single electrons

A model of atoms Schrodinger’s equation shows that electrons can exist in stable configurations around nuclei Wavefunctions and energies for these configurations determine most properties of matter

Mysterious spectrum of light from atoms and all other puzzles completely explained HydrogenHeliumNeon

Key idea: quantum superposition For any two allowed states of any quantum system, the system can exist in a state which is the