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

XXXXELECTRON

XXXX

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 superpositionelectrons can be in two places at once!

Electron at a definite location

Single electron at a superpositionof two locations

Single electron at a superpositionof 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 wavefunctionswill 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 atomsand all other puzzles completely explained

Hydrogen Helium Neon

Key idea: quantum superposition

For any two allowed states of any quantum system, the system can exist in

a state which is the