Why an atom can have nonzero toal angular momentum in the ground state?

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Discussion Overview

The discussion revolves around the question of why an atom can possess nonzero total angular momentum in its ground state, despite having no net electric dipole moment. Participants explore concepts related to symmetry breaking, classical analogies, and the nature of quantum mechanical states.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that the presence of nonzero angular momentum in the ground state may indicate spontaneous symmetry breaking.
  • Another participant draws a parallel with a classical charged rotating ring, arguing that it has no dipole moment but does possess nonzero angular momentum, questioning the uniqueness of this behavior in quantum mechanics.
  • It is noted that orbitals in quantum mechanics can have angular momentum, and if a single electron occupies one of these orbitals, the atom can exhibit nonzero total angular momentum.
  • One participant expresses an intuitive belief that a non-rotating state should be lower in energy than a rotating one, but another counters this by stating that this is not generally true in quantum mechanics.
  • A later reply mentions that if low-energy states with zero angular momentum are filled, electrons must occupy states with angular momentum.

Areas of Agreement / Disagreement

Participants express differing views on the implications of angular momentum in quantum mechanics, with no consensus reached on whether the behavior observed in atoms is special or a continuation of classical principles. The discussion remains unresolved regarding the nature of ground state angular momentum.

Contextual Notes

Participants reference classical analogies and quantum mechanical principles, but the discussion does not clarify the assumptions underlying these comparisons or the specific conditions under which the statements apply.

wdlang
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In its ground state, an atom has no net electric dipole momentum ,but it can have a nonzero angular momentum.

Is this a spontaneous symmetry breaking?

why the ground state is not of zero angular momentum?
 
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A classical, charged, rotating ring has no dipole moment, but nonzero angular momentum.
Why do you expect something special to get the same in quantum mechanics? There are orbitals with angular momentum, and if there are is a single electron in one of those orbitals you get a nonzero total angular momentum.
 
mfb said:
A classical, charged, rotating ring has no dipole moment, but nonzero angular momentum.
Why do you expect that this is something special to get the same in quantum mechanics? There are orbitals with angular momentum, and if there are is a single electron in one of those orbitals you get a nonzero total angular momentum.

intuitively, a non-rotating state is lower in energy than a rotating one
 
Well, this is not true in quantum mechanics, at least not in general. And if the low-energy states with zero angular momentum are filled, electron have to use some with angular momentum.
 

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