Quantum Mechanics

January 10th, 2010 Leave a comment Go to comments

Introduction to Quantum Mechanics

Abstract

There are many many good books about quantum mechanics out there but it seems that they are all nearly inaccessible for the common folks. Especially their content is in most cases not easy to understand.

This article’s intention is to bring the important bits of this very successful theory to the minds of everyone. Formulas will be used of course, but only the very important are visible by default. The derivation of important formulas are included for those who are interested in. But they are hidden by default in “spoiler tags”.

Benefits from Quantum Mechanics

The pros of this theory is it’s ability to describe particles such as atoms and many different things more in a completely new way. Instead of treating everything as point-particles, Quantum Mechanics (QM) describes it as waves. This might sound obsolete to everyone who is familiar with normal physics. But this prediction has been proven to be correct.

Without QM modern chemistry such as pharmaceutics wouldn’t be such successful. Without it, inventions like the magnet resonance imaging or harddisks with a cappacity greater than 20 GB (GMR-Effect) would be impossible.

1. Crisis of classical physics

1.1 Introduction

At the end of the 19th century physicians believed they have found nearly everything which was to find. Newtonean laws of motion and the description of electromagnetismn by Maxwell’s equations had a very great success. But there were some experimental facts which hadn’t fit at all to the theories. These lead to Quantum Mechanics. On this and the next pages I will show you, how it came to the idea of the so called quanta and effects which can only be explained with Quantum Mechanics.

1.2 Black bodies and Planck’s Law or Radiation

If a body is getting hotter, it begins to emit radiation. You can see this best with black bodies (The sun for example is a very good black body). In thermal equilibirium energy density is linked over the radiation and it’s frequency \omega to a temperature T of this body. As it gets hotter it will transmit more and higher energy, starting from invisible infrared going over to red and orange until it reaches white and more bluish colors.

Lets take a perfect black cube which is hollow inside.

The laws to describe the energy density inside it is the Rayleigh-Jeans law.

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But this law leads to unlogic results: It says the total energy in this box has to be infinite. This issue is called the ultraviolet catastrophe.

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Or in other words, if you have a tiny hole in that closed cube an infinite amount of energy comes out of it. This is obviously obsolete.

Finally Max Planck found a solution which avoids this issue.

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He interpreted his solution the following way: Instead of describing energy continuously, it has to be emitted and absorbed in small packages, called the quanta.

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The energy of a single quantum is proportional to it’s frequency with E = \hbar \omega. For light, this quantum is called the photon. And this single quantum is the tiniest unit of energy at this frequency.

This has very wide reaching results which I will explain on the next page.

  1. Scott (sltlamina)
    October 4th, 2008 at 17:06 | #1

    Great job as always, aVoN! Smile Good read.

  2. Block
    October 7th, 2008 at 22:09 | #2

    Now what the hell? We just started a class on this and our teacher really sucks. This helped. Thanks!

    I still had to edit this. I just had one of those “Ooh! Now I get it”- experiences.

  3. October 8th, 2008 at 18:55 | #3

    It’s not easy to understand.
    But don’t forget, this article isn’t finished yet. I’ll add some more chapters later.

    Next planned steps are the photoelectric effect, the wave function, probabilities and then the Schrödinger-Equation.
    After that I’m going to show several examples of solutions of the Schrödinger-Equation.
    And after that, I’ll add a special chapter about one of the most important solutions: Quantum mechanic harmonic oszillator.
    Then the spin and that was all I’ll want to fill your brains with.

  4. Scott (sltlamina)
    October 10th, 2008 at 16:12 | #4

    Fuck yeah! Looking forward to them!

  5. October 11th, 2008 at 01:45 | #5

    I will!

  6. Sorry:D
    February 27th, 2009 at 18:13 | #6

    “”” I just had one of those “Ooh! Now I get it”- experiences.”””

    Ye i totaly love those, altohh this is Nonsence to me i like it Smile nice work

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