I had forgotten the particle in a box problem, and now that I think of of it there are other solutions that have zeros in them. I was thinking more about things like electron density scatter plots that are dense close to the center and drop off asymptotically at large distances. ψ*ψ (a measure of the probability that particle will be in a certain region) never quite gets to zero but can be arbitrarily close. That and tunneling where there should be a zero probability but if fact it is not zero at all. The tunnel diode with its negative resistance characteristic is an example of this.

My undergraduate degree was in Physics. The others are EE and Finance

 

ψ

Tridant??

I plan on taking some physics classes, If I don't go into this it will be EE, I'm pretty sure I have a nack for it.

but, I still have over a year till college, so till then Ill just hope I get calculus as easy as I did algebra and trig.

 

It's the Greek letter 'psi'. ψ(x) is the spatial part of the wave function. When multiplied by its complex conjugate ψ*(x) you get a real function that represents the probability of finding the particle in a region about the coordinate x.

 

So when the wave function is zero the particle is... gone?

 

Not quite. At places in space where the wave function vanishes (has a value of 0), the probability of finding the particle at those locations is zero. Now if the wave function assumes non-zero values in a neighborhood of the zero, there there is a non-zero probability of finding the particle in the neighborhood of the zero.

Check out the Legendre Polynomials for examples of functions with multiple zeros in an interval of interest. In this case the interval is [-1,...,+1]

http://en.wikipedia.org/wiki/Legendre_polynomials

 

The notion is that an object like the electron with spin behaves like things with angular momentum. So you can see why papabravo said what he did -- it's a classical notion and perhaps pedagogically useful. But you have to also reconcile it with the fundamental fact that there is nothing there that is "spinning" in the classical sense. The electron is essentially a point particle. The other key notion, as pointed out on that lovely web page, is that the spin is quantized -- for electrons, it only comes in two flavors. How would you reconcile that with a classical viewpoint? A spinning golf ball, for example, can have a continuous spectrum of angular momentum values, both in magnitude and direction. Not so in the quantum world. That's why these quantum facts are so hard for us to grok -- they're not part of everyday experience. But they're extremely well-established experimental facts.

The idea that the electron is a point in classical physics depends a bit on what classical physics you are using. Actually there is a classical radius of the electron. Assume you have some continuous charge stuff with charge but no mass, take one electrons worth at infinity. Now compress it make ther radius of the infinite blob smaller. As it get smaller the energy goes up. Keep compressing and use e=mc squared. When you hit the mass of the electron stop. This is the classical radius of the electron. Nothing quantum mechanical at all. In this view all the mass is made out of massless charge stuff. This is not to contradict other material in this thread. Just what I think is an interesting note.

 

In this view all the mass is made out of massless charge stuff.

So... the mass... is massless?
thats a new one...

 

http://www.google.com/products/cata...sa=X&ei=sj5wTfHAIdCRgQe8ypA5&ved=0CCYQ8wIwAg#


Was the most understandable book on the subject I've ever read. Give it a go. It just might help you too.

 

http://www.google.com/products/cata...sa=X&ei=sj5wTfHAIdCRgQe8ypA5&ved=0CCYQ8wIwAg#


Was the most understandable book on the subject I've ever read. Give it a go. It just might help you too.

I might, It might help with this like flatland helped with 4 dimensional objects.

 

So... the mass... is massless?
thats a new one...

Not too new, the classical radius has been around for at least 50 years. But then think of a photon, there is no rest mass for it.

 

One of the things I learned early is photons have mass, otherwise they couldn't be affected by gravitational fields. Now they don't. I'm still not adjusted on this one.

Of course, talking about rest mass, photons must move at the speed of light. It is in the definition. The speed can vary a little due to the medium it is traveling in, but it is always whatever the speed the medium can support.

 

How would absolute zero affect things like this?

 

Absolute Zero is a lot like the speed of light, you can can get very close but never achieve it.

The modern methods for cooling matter to make condensates is kinda neat. They use a laser(s) to pick off the more active atoms, pinging them out of the samples, leaving the ones with very low energies. It this range you are talking a degree or so above absolute.