Quantum Theory By: Brian Williams

Blackbody Radiation Around the turn of the 20 th 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? 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 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 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 hypothesis- lambda= h/p

Mathematical Interpretations In the early 20 th 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 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? 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 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 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