If all states are stationary, what causes atoms to radiate then?

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Discussion Overview

The discussion revolves around the question of why atoms radiate light if they are in stationary states, particularly in the context of quantum mechanics and the interaction with the vacuum electromagnetic (EM) field. Participants explore the implications of stationary states, the role of the vacuum EM field, and the nature of atomic eigenstates.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that stationary states of the hydrogen atom do not provide a reason for excited atoms to radiate light, as the Hamiltonian remains constant in time.
  • Another participant argues that the stationary states discussed are specific to the hydrogen Hamiltonian and suggests that including the vacuum EM field alters this, leading to non-stationary states.
  • A question is raised about the nature of the vacuum EM field and its role in triggering light emission from atoms.
  • Further clarification is provided on the vacuum EM field, indicating that it can be incorporated into the Hamiltonian and that its interaction terms can induce transitions between atomic states.
  • A participant questions why atoms are typically considered to be in eigenstates of the atomic Hamiltonian rather than the full quantum electrodynamics (QED) Hamiltonian.
  • Another participant suggests that the presence of a superposition of states leads to non-stationary behavior, as an ensemble of atoms can occupy multiple excited states.

Areas of Agreement / Disagreement

Participants express differing views on the implications of stationary states and the role of the vacuum EM field, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

There are limitations regarding the assumptions made about the Hamiltonians involved, the definitions of stationary and non-stationary states, and the specific conditions under which these discussions apply.

Who May Find This Useful

This discussion may be of interest to those studying quantum mechanics, particularly in the areas of atomic physics and quantum electrodynamics.

Raziel2701
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We've solved for several systems, the hydrogen atom for instance, and one of the properties of these is that it doesn't matter what excitation state you look at, they are stationary states, the Hamiltonian is constant in time, so where's the impetus on an excited atom to radiate light if it's in a stationary state?
 
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The stationary states you solved for are for the hydrogen Hamiltonian only. If you included the vacuum EM field, then they would not be stationary states. All "spontaneous emissions" are the result of stimulated emissions except with the vacuum EM field.
 
So, what is this vacuum EM field? How does it trigger emission of light in the atom?
 
So, what is this vacuum EM field?
Include the electromagnetic field by adding the term ½(E2 + B2) to the Hamiltonian. Initially the EM field is in the vacuum state (no photons).
How does it trigger emission of light in the atom?
Add the interaction terms to the Hamiltonian:

(1/2m)(p - eA)2 + eφ

These terms have nonzero off-diagonal matrix elements which induce the transition between the excited state ψ1 and the ground state ψ0
 
Then I wonder, why usually an atom is in an eigenstate of H_atom, instead of an eigenstate of the full QED hamiltonian?
 
I always thought it was because the superposition of states was non-stationary, so if you had an ensemble of atoms with a given energy distribution, the possibility that anyone could be in any of a multitude of excited states is what causes the superposition, and hence non-stationary state
 

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