Quantum Theory
By: Brian Williams
Blackbody Radiation
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Around the turn of the 20th century, physicists were
studying the total energy carried by all of the
electromagnetic radiation inside an oven at a given
temperature
Using classical physics, scientists came up with a
ridiculous answer, infinity!
Max Planck came up with a solution- energy can only be
emitted in small packets, called quanta, and the energy of
each wave is determined by its frequency
Light- Particle or Wave?
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Particle
First thought of by
Newton, who suggested
that light was made up of
little “bullets”
Later verified by Einstein
in his Photoelectric Effect
Energy of each photon is
given by E=hf
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Wave
First proposed by
Christian Huygens, a
colleague of Newton’s
Verified by Thomas
Young in 1803, using a
modified version of the
double-slit experiment
Double-Slit Experiment
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When one slit is opened, the
photons appear directly in line
with that slit
But when both slits are
opened, the photons form an
interference pattern
This result holds even if you
there is only one photon in the
system at any given time
Works with electrons as well!!
De Broglie’s hypothesislambda= h/p
Mathematical Interpretations
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In the early 20th century, scientists
were looking for a mathematical
construct that could describe
atomic systems
In 1925, Erwin Schrodinger wrote
down the equation shown on the
left, which is known as the
Schrodinger equation
Around the same time, Werner
Heisenberg developed matrix
mechanics, an equally valid
method
Later, Paul Dirac showed that the
two were equivalent
Particle in a Box
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The Schrodinger equation can be used to solve for the
probabilities, not the actual position of the particle
Once you get the wave equation, you can square it to get a
probability density of where the particle might be
Quantum mechanics can only tell you the statistical
probabilities of certain outcomes or positions, not because
of any flaw in the theory, but because this is the way
nature works!
In order to know for certain where the particle is, you
must observe it
Which brings us to our next question…..
Where was the particle?
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If you know where the particle is now, at position C,do you know
where it was right before you looked at it?
3 common interpretations
1. Realist position- Advocated by Einstein, among others. The
particle was always at C. “The position of the particle was never
indeterminate, but was merely unknown to the experimenter”
2. Orthodox interpretation- Advocated by Niels Bohr. The particle
wasn’t really anywhere. The act of measurement (looking at it)
forced the particle to “decide” on a definite position. Observations
not only disturb the particle, they produce it
3. Agnostic interpretation- Advocated by Wolfgang Pauli. Asserts
that this question is metaphysical and cannot be answered, it’s a silly
question that should not even be bothered with.
So, which is correct?
Schrodinger’s Cat
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Imagine a cat inside a steel chamber, along
with this device. In a Geiger counter there
is a tiny bit of radioactive substance, so
small that perhaps in the course of one
hour one of the atoms decays, but also,
with equal probability, perhaps none; if it
happens, the counter tube discharges and
through a relay releases a hammer which
shatters a small flask of hydrocyanic acid,
thus killing the cat
Now, without opening the lid of the box, is
the cat alive or dead?
Yes.
A Few Quotes to Ponder
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Albert Einstein- “God does not play dice with the Universe.”
Neils Bohr- “Albert, stop telling God what to do!”
Bohr- “Anyone who says that they can contemplate quantum
mechanics without becoming dizzy has not understood the concept in
the least.”
Richard Feynman- “There was a time when the newspapers said that
only twelve men understood the theory of relativity. I do not believe
there ever was such a time. There might have been a time when only
one man did because he was the only guy who caught on, before he
wrote his paper. But after people read the paper a lot of people
understood the theory of relativity in one way or another, certainly
more than twelve. On the other hand, I think I can safely say that no
one understands quantum mechanics.”
The End