1. DUALITY
PARTICLE
WAVE PARTICLE DUALITY
WAVE
John Parkinson

2. TOMAS YOUNG 1805 INTERFERENCE EXPERIMENT
constructive interference
destructive interference

3. Light must be a wave min max min max min max min
Light behaves like water waves in a ripple tank
min
max
min
max
min
max
Light must be a wave
min

4. Light can be diffracted
circular aperture
light
Light must be a wave

5. LIGHT MUST BE A PARTICLE!
Photoelectric Emission! e
Photon of Light
potassium metal

6. LIGHT
PARTICLE OR
WAVE OR
WHAT?

7. ENERGY IS CONTINUOUSLY VARIABLE
PRE 1900 CLASSICAL THEORY
1900 PLANCK’S QUANTUM THEORY
AT THE ATOMIC LEVEL ENERGY IS QUANTISED, IT CANNOT HAVE ANY VALUE

8. PHOTONS E = h f but c = f λ Light comes in packets of energy.
EINSTEIN (1905):
Light comes in packets of energy.
PHOTONS
0.3 M
E = h f
ENERGY OF A PHOTON is
but c = f λ

9. N.B. a photon has zero rest mass
combining
and
So the effective mass of a photon is given by
For yellow light with λ = 550 nm,
N.B. a photon has zero rest mass

10. THE IMAGE IN A DIGITAL CAMERA IS BUILT UP AS EACH PIXEL REACTS TO A PHOTON.
2.5 k
photons
10 k
photons
100 k
photons
1 M
photons
4 M
photons
25 M
photons
The wave nature of light cannot account for individual pixels in camera being hit.

11. i.e. the wavelength of a photon is Planck’s constant divided by its momentum, p .
1923 : Louis de Broglie : “If a photon behaves as particle with mass, then a particle should have an associated wavelength given by
where v is the particle’s velocity

12. Test: Can electrons be diffracted?
An electron has a small mass, like a photon; might it behave as a wave ??????
Test: Can electrons be diffracted?
heater
graphite target
vacuum e
YES, ELECTRONS DO HAVE A WAVE NATURE

13. Wave-Particle Duality
wave function
particle
wave function
particle
wave function
particle
wave function
What is light? What is an electron? Are they schizophrenic?
ARE THEY PARTICLES?
ARE THEY WAVES?
ARE THEY PARTICULATE WAVES?
ARE THEY WAVY PARTICLES OR WAVICLES?
It depends on the experiment you’re doing !

14. A Moving Particle in Quantum Theory

15. Example: de Broglie wavelength of an electron
Mass = 9.11 x kg Speed = 1 x 106 m s-1
This wavelength is in the region of X-rays
and is about the size of an atom

16. Example: de Broglie wavelength of a ball
Mass = 1 kg
Speed = 1 m s-1
This is extremely small! Thus, it is very difficult to observe the wave-like behaviour of ordinary objects. Quantum Effects only becomes important at the microscopic level of atoms

17. MATTER WAVES AN ELECTRON FIRED AT A DOUBLE SLIT
screen
interference pattern
the ELECTRON must travel through BOTH slits!
IF WE TRY TO FIND OUT WHICH SLIT THE ELECTRON TRAVELLED THROUGH THE ELECTRON LOSES ITS WAVE NATURE, BECOMES A PARTICLE, AND PASSES THOUGH JUST ONE SLIT.
Heisenburg’s Uncertainty Principle: It is impossible to determine the position and the momentum of a given particle at any particular time, as attempting to find one of these quantities will disturb the other.

18. Given ONE electron, we cannot predict exactly where it will hit.
We can only predict the PROBABILITY that it will hit a certain place on the screen: hence we can only predict the pattern that many electrons will make!!
Real photographs of an electron interference pattern with increasing numbers of electrons… 10
100 2k
20k
80k
The electron’s wave nature producing an interference pattern
If we don’t look, the electron goes through both slits. If we do look it chooses one.

19. HOW THE PATTERN BUILDS UP
SCREEN
Because of the Uncertainty Principle, we cannot predict where an electron is at any time.
We can only talk about probability functions. Quantum Mechanics says the probability of something being in a certain place at a certain time is proportional to the square of wave function’s amplitude. When an electron passes through the double slit, its probability function splits up into two, then the two parts interfere with one another. The electrons pass through both the slits simultaneously. (Provided that no one is observing. If someone is watching, the electrons behave as particles).
Protons and neutrons have been observed to behave similarly

20. Summary
Light is made up of photons, but in macroscopic situations, it is often fine to treat it as a wave.
When looking at the microscopic world, there is only one thing that works… Light is made up of photons which have duality.
Photons carry both energy & momentum E = hf or E = hc / λ
Matter also exhibits wave properties. For an object of mass m, and velocity, v, the object has a wavelength λ = h / mv
Depending on the experiment an electron can behave like a : e-
wave (interference and diffraction)
particle (localized mass and charge)

21. Schrödinger’s Cat If we open the box could we kill the cat?
In 1935, Erwin Schrödinger proposed a "thought experiment" to highlight one of the ways in which quantum mechanics contradicts our experiences of reality. His proposal involved placing a cat (a macroscopic object) inside a closed box with a vial of cyanide and a radioactive atom initially prepared in the metastable state (a microscopic object). The radioactive atom has a probability of ½ of decaying in one hour. If it decays, then the cyanide is released and the cat dies; if it does not decay, then the cyanide is not released and the cat remains unharmed.
The paradox arises because the atom, being a microscopic object, must be described by quantum mechanics. After one hour, and before it is observed, the atom is in an equal superposition of being decayed and undecayed. However, if quantum mechanics is a universal and complete theory, it must describe the whole system. And, since the state of the cat is correlated with the state of the atom, the cat must also be in a superposition of being dead and alive.
If we open the box could we kill the cat?