Notes: A (Very) Brief Introduction to Quantum Mechanics

In an uncharacteristic act of efficiency, I have finally gotten around to organising my notes into a fashion approaching orderly. So, I thought to myself, why not do some revision while the notes are out? So here we are. What shall we do? I'm feeling a in bit of a quantum stuff kind of mood. I'll just change the title there and let's get on with it, shall we?

I don't think I've delved much into QM at all here, so here is a quick comparison with it and the classical kind.

Classical Mechanics

• The Newtonian sort. You have a particle with a position in space and a momentum. These are things that can be measured, calculated, and ultimately known.
• Generally it's applied to objects at a more macroscopic scale, stuff we can see around us, moving at reasonable velocities.
• It's therefore obvious to us and somewhat intuitive. You throw a ball, it moves as you'd expect with the energy you transfer into it. That ball hits your inattentive friend in the face and you can kind of predict that energy is going to be transferred into your friend's face as the ball comes to an abrupt halt.

Quantum Mechanics

• The position of a particle can be known if it is measured, but doing so means we cannot measure it's momentum to a similar degree of accuracy. This isn't so much that we don't have the equipment to do it as it is that the maths just doesn't work out.
• Here we are generally dealing with things on a more atomic scale, and not of things of our everyday ken.
• Subsequently you can expect it to be somewhat counter-intuitive.

The next thing you must understand is that it is a theory. It is a framework that allows us to make predictions and calculations on things beyond our aforementioned ken, but it must still be backed up by experiment. It has also thus far never been proven wrong. So, a pretty sound model, wouldn't you say?

This has nothing to do with anything in this post.

A quick history

Back in the 19th century there were some physical problems going about. Gustav Kirchoff had proven the concept of a black body, an object that absorbs all light, and thus would appear black to an observer. He also proved that the energy emitted E depends only on the temperature T and the frequency v of the emitted energy. He challenged physicists to find the specific function that could describe this.

Many attempts were made but it was not until Planck, following a visit from fellow physicist Heinrich Rubens in 1900, came up with the idea that light could be broken into separate "quanta" that things really got underway. Quick rundown time.

1905, Einstein (Big hair, kind of a big deal, you know the guy) was working on the photoelectric effect and realised that while electromagnetism wasn't working too well, Planck's idea about quanta might be a better bet. This realisation earned him the 1921 Nobel prize, which I imagine was nice for him.

1913, Neils Bohr made some pretty groundbreaking work regarding the spectral lines of Hydrogen. This was opposed by the old fuddyduddies, but the younger guys, Rutherford, Einstein and the like were pretty impressed by it all.

1924, Bohr et al propose more stuff. This all tuns out to be wrong, but it does provide plenty of precious precious experimental data.

1925, Heisenberg publishes a paper demonstrating that the observation of the position of a particle would ultimately change it's momentum. In doing so he uses matrices, shocking everyone who thought that matrices were solely the domain of those mathsy wankers.

1926, Paul Dirac fully derives Planck's law, and the idea of causality in physics is slowly being abandoned. Regarding collision Max Born wrote:

One does not get an answer to the question, What is the state after collision? but only to the question, How probable is a given effect of the collision? From the standpoint of our quantum mechanics, there is no quantity which causally fixes the effect of a collision in an individual event.

Later Einstein would write a letter to Born where he would spawn the famously paraphrased assertion:

Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that He does not play dice.

Now, I ask you, who the devil decided that "God does not play dice" was a better summary that "The Old One does not play dice"? It's right there in the quote guys. How the Almighty did you fuck that one up?

Anyway, Einstein continues to prove himself a belligerent old sod by arguing extensively about the matter. This is not really a bad thing, as in his eyes the theory's foremost supporters were basically sitting back and going "Well, that's that. Everything is shiny." Einstein was really just loudly explaining that he just didn't get it, and shouldn't we really be ironing out these questions before declaring the work done? He didn't want the Uncertainty Principle to become physics' "A wizard did it". 

This kicked off a series of arguments and thought experiments that came to be known as the Bohr-Einstein debates.

 "It is wrong to think the task of physics is to find out how nature is," said Bohr. Einstein disagreed. "What we call science," he said, "has the sole purpose of determining what is."

So, experiments were done, theories were made, and this has continued ever since. It is still our best theory for what happens at inconceivably small scales, and working with it hasn't made our quantum dependent electronics blow up (Note: I'm referring to basically all popular electronics. Reading this? Thank quantum mechanics.)

That'll do for now I think. I hope you find yourself intrigued, or at the very least a little more informed. That's all we ask here at EP.  Late'