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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.

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quantum superposition

Quantum Superposition

Mark Van Raamsdonk

the quantum world
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!


Atoms would be unstable by classical rules

Orbiting charge would produce EM radiation

This carries away energy

Electron losing energy spirals into nucleus

All atoms would cease to exist in a nanosecond

the double slit experiment
The double slit experiment

Bright line appears directly between the slits,

with other bright lines to the sides

explain via wave interference
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



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

surprise same result for electrons
Surprise: same result for electrons

more electrons



less electrons



Electrons behave like waves??

Interference between different electrons going through the two slits?? (No!)

explanation quantum superposition electrons can be in two places at once
Explanation: quantum superpositionelectrons 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
The wavefunction

Mathematically, we describe a quantum superposition by a function Y(x)

Y largest here

Y zero here

Y is larger/smaller in magnitude in places where we are more/less likely to find electron

schrodinger s equation
Schrodinger’s Equation

Determines how wavefunctions

will evolve with time

Correctly explains double slit experiment in terms of single electrons

a model of atoms
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

Hydrogen Helium Neon

key idea quantum superposition
Key idea: quantum superposition

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