- #1
eoghan
- 207
- 7
Hi there!
If I want to find the eigenstates of the hydrogen atom in QM I start with the hamiltonian of a free particle in a Coulomb potential. But an electron in a coulomb potential is stable in classical mechanics too! The instability of the system comes from the fact that the electron accelerated radiates energy away. So, in the quantum hamiltonian shouldn't I consider also the energy radiated away by the accelerated charge?
I mean, if I consider only the hamiltonian:
[tex]H=\frac{P^2}{2m}-\frac{e^2}{4\pi \epsilon_0 r}[/tex]
it is as I am considering in classical mechanics only the force:
[tex]m\ddotx=-\frac{e^2}{2\pi\psilon_0 r^2}[/tex]
and I don't consider the energy radiated away, so if I solve this equation I get stable orbits!
If I want to find the eigenstates of the hydrogen atom in QM I start with the hamiltonian of a free particle in a Coulomb potential. But an electron in a coulomb potential is stable in classical mechanics too! The instability of the system comes from the fact that the electron accelerated radiates energy away. So, in the quantum hamiltonian shouldn't I consider also the energy radiated away by the accelerated charge?
I mean, if I consider only the hamiltonian:
[tex]H=\frac{P^2}{2m}-\frac{e^2}{4\pi \epsilon_0 r}[/tex]
it is as I am considering in classical mechanics only the force:
[tex]m\ddotx=-\frac{e^2}{2\pi\psilon_0 r^2}[/tex]
and I don't consider the energy radiated away, so if I solve this equation I get stable orbits!