acronymsical
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Did you do your homework yet? May I check it?
Famous words of my mother. Of course I did my homework. But I wasn't in bed until 7:30 this morning. I did solve #3. This I am proud of. So proud in fact that I am going to show it to you. Not sure if it's quite right, but I think it's at least close.
So here's the situation, before I get into the nuts and bolts. A Hydrogen atom has one proton, with positive charge, and one electron, with negative charge. The electron orbits the proton. If we assume the proton is infinitessimally small, we can solve this problem exactly using mathematical techniques. And we get an answer. But it's not quite perfect because even something as simple as the Hydrogen atom is always more complicated than it first appears. My homework question was to determine "to first order" (meaning figure out most of it) what happens if we allow the proton to be spherical instead of just being a point. This is quantum mechanics. Things are not necessarily as they appear. In the world we're used to, this would not change the answer at all. The electron would still orbit the proton in exactly the same way. If we suggest that the proton is a sphere, there's still nothing to prevent the electron from going through the sphere on its way around the atom. Aside from its electric charge, the proton has no other effect on the electron. So this is the calculation. The size of the proton is represented by lower case greek letter rho (looks like a lower case 'p'). This is what I spent all last night doing. Of course, the solutions are typed. I may explain the wonders of the typesetting program LaTeX later.
So here's the situation, before I get into the nuts and bolts. A Hydrogen atom has one proton, with positive charge, and one electron, with negative charge. The electron orbits the proton. If we assume the proton is infinitessimally small, we can solve this problem exactly using mathematical techniques. And we get an answer. But it's not quite perfect because even something as simple as the Hydrogen atom is always more complicated than it first appears. My homework question was to determine "to first order" (meaning figure out most of it) what happens if we allow the proton to be spherical instead of just being a point. This is quantum mechanics. Things are not necessarily as they appear. In the world we're used to, this would not change the answer at all. The electron would still orbit the proton in exactly the same way. If we suggest that the proton is a sphere, there's still nothing to prevent the electron from going through the sphere on its way around the atom. Aside from its electric charge, the proton has no other effect on the electron. So this is the calculation. The size of the proton is represented by lower case greek letter rho (looks like a lower case 'p'). This is what I spent all last night doing. Of course, the solutions are typed. I may explain the wonders of the typesetting program LaTeX later.
No invariants - Fancy your favorite symmetry group.
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