Is There a Relationship Between Principal Quantum Number and Amplitude?

[rauletechuleta]

The principal quantum number refers to the energy of the electron in an atom, and the average distance of the electron from the nucleus. It seems to me to be analogous to the concept of amplitude for a classical wave. Is there a relation?

 

[ZapperZ]

The principal quantum number refers to the energy of the electron in an atom, and the average distance of the electron from the nucleus. It seems to me to be analogous to the concept of amplitude for a classical wave. Is there a relation?

This is such a vague similarities. It is like claiming that a cow is analogous to a basketball just because from very far, the cow looks like a sphere.

To be able to make such comparison, you have to show somehow that "n" is related to the amplitude of some kind of a wave. This is not true if you solve for the Schrödinger equation for the H atom, let's say. "n" doesn't strictly represent the amplitude. It does, however, relates to an eigenvalue.

Furthermore, to be complete, it refers to the "energy" of the energy level only in the degenerate case. One can remove the degeneracy via external fields, and including spin-orbit coupling in the atom.

Zz.

 

[rauletechuleta]

It doesn't seem like claiming that at all. Your comparison refers to the way the eye's technical limitation prevents the subject from discerning the correct shape of something at a distance. In your example, a basketball would not be analogous to a basketball if you saw them at different distances. Your example is more about perception, while my question is more about definition.

I'm going to check out what an eigenvalue. Thank you ZapperZ

 

[ZapperZ]

It doesn't seem like claiming that at all. Your comparison refers to the way the eye's technical limitation prevents the subject from discerning the correct shape of something at a distance. In your example, a basketball would not be analogous to a basketball if you saw them at different distances. Your example is more about perception, while my question is more about definition.

But that is, in effect, what you are using, a "perception" of the connect of "n" to the amplitude of a classical wave. There's nothing in the mathematics, if you look at the wavefunction of a H atom, for there to be any kind of resemblance between the two.

Zz.

 

[rauletechuleta]

Thank you.