What if the intensity is really small?
Wimpy Laser beam: P = 3·10-19 W
First photon
strikes here
Where’s the photon?
Great question!
But no one can answer it/
It will strike the screen at an undetermined position!
3rd/
Next photon
strikes. here
..
screen
If the laser power is 3·10-19 W, we get only about one photon
per second in the beam! (assuming red light)
Where's that one photon?
Well, we don't know until it strikes the screen.
Most photons hit the screen where intensity (i.e. |Emax|2) is highest.
Remember the two slit interference?
However: We do observe that more photons strike at the
places where the intensity of the laser beam
is largest.
Important conclusion:
The probability to find a photon at a specific location in a
beam of light is proportional to the intensity (or: ∝|Emax|2)
of the beam at that location.
Probability is proportional to |Emax|2
Probability and randomness
Photon is 3-D-spread-out-little-chunk of an EM wave.
Gazillions of electrons in metal:
Which one will be kicked out?
Can’t tell, but photon uniformly
spread out so equal probability
everywhere.
What if shape of single photon wave looked like this?
Gazillion electrons
Which one will be kicked out?
Answer: Can’t tell, but probability
of ‘photon collapse’ at particular
point (kicking out electron) related
to intensity of wave (Emax2)
Probability of photon hitting is related to intensity at that location
(electric field strength)2~Intensity &
proportional to the probability of where photon will hit!
standard electric field
representation of light field
Classical electric field wave
pattern describes probability
of where photons will be
Higher intensity means higher
likelihood that photons will be
detected there.
If I shoot a photon through the two slits to hit the screen, it has some
chance of being detected anywhere on screen, but on average better
chance at being where interference pattern in brightest.
What if I turn-down the intensity
so much that I only have one
photon at a time? Do I still get
an interference pattern?
Which slit did this photon go through?
Double slit experiment at low intensities
(Here: for electrons, actually/)
If one slit:
Get single slit pattern
(i.e. no interference)
Like this:
or this:
but not like this:
But: that photon is part
of the two slit interference pattern.
The probability pattern of where it lands is described by the 2 slit
interference pattern (the photon has to ‘know’ about both slits!)
It must have gone through both slits, i. e. as a wave!
(When it interacts with the screen it behaves particle-like!)
quantum-wave-interference_en.jar
Double slit experiment at low intensities
Double slit experiment at low intensities
(Here: for electrons, actually/)
(Here: for electrons, actually/)
Double slit experiment at low intensities
Double slit experiment at low intensities
(Here: for electrons, actually/)
(Here: for electrons, actually/)
Photon before it goes through the slits
Photon as little segment of
wave moving towards slits
Photon after it went through the slits
Still only one photon!
(But this photon has
a slightly complicated
wave function.)
Photon is a wave/
It can interfere with itself.
Intensity of wave in various places, indicates probability
of finding the photon there if you looked at that moment.
Photon after it went through the slits
When photon interacts with
one electron or atom, all
energy ends up in one
spot/ Behaves like a
particle with energy = hc/λ
Intensity of wave in various
places indicates the probability of
finding the photon at that spot, if I
had detector there (e.g. a bunch
of atoms or a sheet of metal)
Probability of photon hitting is related to intensity at that location
(electric field strength)2 ~ Intensity &
proportional to the probability of where photon will hit!
standard electric field
representation of light field
Classical electric field wave
pattern describes probability
of where photons will be
Higher intensity means higher
likelihood that photons will be
detected there.
If I shoot a photon through the two slits to hit the screen, it has some
chance of being detected anywhere on screen, but on average better
chance at being where interference pattern is brightest.
Randomness in physics??!
A completely new concept in QM is that the outcome of a
measurement can often times not be predicted precisely.
We can only predict the probability of
obtaining a certain result!
Examples:
Where will a photon hit the screen?
Well, we don’t know, but the probability is largest where
the intensity of the light is largest ∝ (field amplitude)2
Where is the electron in a hydrogen atom?
Well, we don’t know, but the probability to find it is
largest at the location where the square of the matter
wave amplitude is largest. (Matter waves: see TZT chapter 6)
(Randomness is negligible for macroscopic objects but important on atomic scale!)
To all those students feeling confused now:
You should be bothered and ask questions!
The Particle-Wave duality is kind of confusing @ 1st.
QM: Fundamental change in the way to think about physics:
Before (pre 1900, Physics I and II) -- everything could be
known exactly, if measured and calculated carefully enough.
Now-- physics behavior is fundamentally inexact.
Talks only about probability; Can only predict
probabilities for what will happen in a measurement.
Einstein didn’t accept this fact for long! And he certainly
was a pretty bright fellow! Today we fully accept the QM
description of small things (This was not the case at first!)
Remember this picture?
Scanning tunneling microscope (STM)
Measure current
between tip and
sample
Electrons are wave packets too!
What’s next?
Atoms and atomic spectra!
The probability to
find an electron that
is trapped inside this
ring of atoms is
highest at the place,
where the square of
the amplitude of the
electron wave
function is largest.
What happens if we bash atoms with
electrons?
In atomic discharge lamps, lots of electrons are given kinetic
energy (accelerated by a high voltage). When they bash into
atoms some of this kinetic energy is transferred to the atom
Atom get's excited!! (“Neon” lights, Mercury street lamps)
120V
Cathode (hot metal, so
electrons can come out)
Anode (positive potential)