Transcript Constructive Interference

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
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
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
more electrons
XXXX
XXXX
less electrons
XXXX
ELECTRON
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 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
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
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