Thread: The Bohr Model
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loandbehold
loandbehold is offline
#12
Nov26-04, 06:17 AM
P: 13
Quote Quote by marlon
I am sorry but i don't think that you really know what you are talking about.

The orbits have their specific form because of effective potential energy (at least in the most easy model). I know this is very vague so let me elaborate by taking the simplest configuration possible : The H-atom : 1 positive nucleus and one orbiting electron. Their potential is Coulombic in nature and if you were to plot the effective potential of the Schrödinger-equation as a function of the inter-particle-distance r, you will get a curve that exhibits a minimum at a certain distance between the two particles. This distance is the socalled Bohr-radius for a Hydrogen-atom in the GROUNDSTATE. So when an electron is at this specific distance from a nucleus with one proton, the entire system will be in a state of minimal potential so it is most stable. This is the reason why no collapse takes place. All these calculations are made via time-independent perturbationtheory where the perturbed Hamiltonian expresses the two-particle-interaction...
Probably not, but I don't understand what your objection is either.

For a hydrogen atom the way the problem is usually presented is to solve the Schrodinger equation for a Coulomb potential [tex]V(r) \propto -1/r[/tex]. Doing this gives rise to a set of eigenstates and eigenenergies, the lowest of which corresponds to the 1s orbital. In my ignorance, I'd blithely assumed that this was the ground state, and that the reason why this state is stable is due to the fact that there is no lower energy state for it to decay to. Are you saying that this is incorrect?

Of course this is not the whole story since you also have corrections to the Hamiltonian due to things like relativity and spin-spin interactions between the electron and proton. But my understanding was that these will only perturb the eigenstates and eigenvalues slightly, and that you would still have a ground state even if you don't include these corrections.

I don't understand what you mean by the "effective potential of the Schrodinger equation" in this problem. Could you elaborate on this please?