Wave Mechanics Comment
I am interested in quantum mechanics and have done some reading into it before I looked it up on the internet. Yours is the first site I have seen which actually explains QP in words. A very top notch page and some very good explanations, however it has come to my attention that (only from what I have learned) a good deal of your information is being taught wrong. The mention of wave mechanics is outdated. This method will give you the right answers however you are using a method which is not factual the particles do not exist in those planes because they need a full wave it is because they contain a certain quanta of energy since quanta only come in steps there are no in betweens, just like in your wave example (half waves don't exist) The entire idea of wave mechanics is incorrect although it does work for calculations, but not in experiments.
Perhaps you are confusing the difference between non relativistic quantum mechanics (the Schrodinger wave equation) and the relativistic formulation put forth by Dirac which relies also on the matrix theory. The wave mechanics gives us atomic physics quantities including the bound state energies to very good accuracy. There are small corrections that come about because of the not-so-non-relativistic electron speed but at that stage such effects as the hyperfine adjustments from the nucleus spin etc also come into play.
There is no rigid wall of course but the energy levels are indeed found by solving a boundary value problem where the solution (wave function) must satisfy the Schrodinger equation with the true potential instead of a brick wall and perhaps other boundary conditions such as the wave function being a certain value at the origin for example.
When one looks at the level (energy or size) of the individual particles (10^-15 meter, 1 GeV), such as in nuclear or high energy reactions such as seen at Fermilab then yes, you must deal with the relativistic equations but you are still really dealing with particles as such.
If there is an experiment which you believe does not fit this, please send me a reference.
Another thing I noticed(please son't take this wrong) was that you said electrons have spin. You did a good job describing this aspect of an electron, however from what I know you were incorrect when you said that the electrons actually spin. The term spin was arbitrarily chosen by its discoverer. If he had called it jump the electrons wouldn't actually be jumping. Please don't take this wrong I'm just a 16 year old high school student I'm probably wrong in my assumptions ( if I am please explain them to me)
Perhaps the wording was awkward on that web page you refer to. You are correct about this. If electrons had a physical nonzero size then they could have a mechanical spin in addition to any angular momentum or quantum mechanical spin. They don't though.
sorry if I'm wasting your time Hinton Williams
You are never wasting our time. The point of research is to impart knowledge on the human race. If all scientists did was write numbers in labbooks without trying to teach interested young students like yourself what makes the world tick, I don't know what kind of world it would be.
Glad you are interested,
PS Please let us know about errors or suggestions like these on web pages as we are trying to make them as useful as possible.
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