Does the shape of atomic orbital changes when exposed to electric or magnetic field?
What do you think?
Where does the orbital come from (solution of which equation)? How does that equation change when there is an external field?
No and yes. The distances of electron clouds is quite short and the forces very strong. No magnetic field in everyday experience changes their shape in any non-negligible way. As DrClaude pointed out though, look at what the equations do when you introduce a magnetic field.
Magnetars are the super heavyweights of magnetism and do some wonky things to atoms. Hydrogen atoms stretch 200 times their normal length and distort electron clouds so much that chemistry becomes impossible. https://en.m.wikipedia.org/wiki/Magnetar
This is incorrect. See, e.g., https://en.wikipedia.org/wiki/Magnetic_dipole_transition
It's weaker than an electric dipole transition, but it's comparable to an electric quadrupole transition.
It's also worth pointing out that the field doesn't have to be time-dependent in order to perturb the electron motion. Think of the Hamiltonian for an electron in a B field with an added 1/r potential term.
Interesting. The article Looks like it's talking about quantum effects of an electromagnetic wave. Does this apply to a static field? The original post to be is describing something like an atom next to a bar magnet.
Yes. In the link I provided above, none of the terms in the Hamiltonian are required to be time dependent. Think about the motion of a free electron in a static B field, then add a 1/r potential for the nucleus. In fact, even without the electron's spin, you get coupling between the magnetic field generated by the electron's orbital angular momentum and the B field (assuming L≠0).
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