Some fundamental questions on light matter interactions

[110010]

Hi there,

I've a few (probably very basic) questions about photon-electron (light-matter) interactions. Here we go:

1) How can an electron "understand" that the frequency of incoming photon is equal to its excited state and so absorb that. Is there any "virtual" resonance between the electron and its excited level so a photon with the same resonance frequency can interact with the electron & electron's excited state system?

2) Why (or how) do refractive index of a medium differs for light with different frequencies? It's probably related with energy conversation or something but I cannot get it.

Mathematics of these questions are OK but I cannot understand these facts in a physical sense of manner.

Thanks in advance.

 

[mfb]

1) How can an electron "understand" that the frequency of incoming photon is equal to its excited state and so absorb that. Is there any "virtual" resonance between the electron and its excited level so a photon with the same resonance frequency can interact with the electron & electron's excited state system?

Quantum mechanics. You can calculate it, but I don't think there is an intuitive model for this. Rabi oscillations are a bit like your description, but they have a different frequency.

2) Why (or how) do refractive index of a medium differs for light with different frequencies?

Polarization can vary with frequency, especially close to resonances in the material.

 

[110010]

Thank you for the answers mfb.

Then, for the first question, in quantum mechanics we can describe what is going but cannot why or how it is going on, right?

Quantum mechanics. You can calculate it, but I don't think there is an intuitive model for this. Rabi oscillations are a bit like your description, but they have a different frequency.


Polarization can vary with frequency, especially close to resonances in the material.

 

[mfb]

Physics cannot answer "why". It can describe things on very fundamental levels, but all theories are just based on observations and made to describe those observations.

 

[Bill_K]

Physics has no answer to the ultimate "why", but it can reduce the number of independent "whys" that go unanswered! Saying it's "simply because of quantum mechanics" -- we can do better than that.

How can an electron "understand" that the frequency of incoming photon is equal to its excited state and so absorb that. Is there any "virtual" resonance between the electron and its excited level so a photon with the same resonance frequency can interact with the electron & electron's excited state system?

Forget about the frequency of the photon and focus on the energies involved. A state with a well-defined energy evolves according to the Schrodinger equation with a well-defined frequency, but the states involved are not just the photon by itself, they are all electron + photon. And so the relevant frequency pertains to the combined energy.

Consider two states: (a) electron in the ground state, plus photon going by, and (b) electron in the excited state by itself. If it's the "right" photon, (a) and (b) have the same total energy. As long as we ignore the coupling term, (a) and (b) are degenerate eigenstates and evolve independently of each other. The transition never takes place But if we now add the coupling term, (a) and (b) behave like a pair of coupled harmonic oscillators, and gradually evolve into one another. This happens only if the energies of (a) and (b) match, i.e. if and only if the "right" photon happens by.

 

[Naty1]

Hi 110010...
the most intuitive explanation I've seen is via standing waves:

[Wikipedia has this introductory explanation

The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves. The lowest possible energy an electron can take is therefore analogous to the fundamental frequency of a wave on a string. Higher energy states are then similar to harmonics of the fundamental frequency.

http://en.wikipedia.org/wiki/Atomic_orbital


Think of a violin string as an analogy: the ends are constrained, so it can have only certain tones...certain vibrational patterns and associated energies. it's energy levels are constained to certain values...it's degrees of freedom are limited.

Another helpful analogy is to think of the electron as a wave...when it's in free space the wave is everywhere, it extends all over the place. But when attracted by a proton in a nucleus, for example, that wave is now localized...it's constrained and so its different from the free space case. And the constraint is also modified by the presence of other electrons and additional protons. Since the energy is contained in the wave, changing it's configuration via the presence of nearby particles changes the wave characteristic and likely energy levels. It's very unlikely for the electron to be found between allowed energy levels.

When a particle is part of an atom or a larger structure, it's constrained...it's degrees of freedom are determined and limited by the whole structure. So electron energy levels and degrees of freedom are determined by the numbers of protons in the nucleus as well as the particular structure of a lattice, as examples. The Schrodinger wave equation describes these.


tomstoer posted this related description:

In an atom it's not the [bound] electron that absorbs the energy of the incoming photon but the whole atom; the usual QM description of the hydrogen atom is a bit misleading here b/c it treats the proton classically, but it should be clear that a more realistic picture is a two-particle Schrödinger equation where the proton-electron system as whole can absorb the photon whereas a single, free electron can't due to energy-momentum conservation... for a particle to absorb a photon you need internal degrees of freedom which can be excited. A free electron can't absorb a photon due to the non-existence of these inner degrees of freedom. An electron bound in an atom can b/c the whole atom (proton-electron bound state) provides these inner degrees of freedom.

Think of a violin string as an analogy: the ends are constrained, so it can have only certain tones...certain vibrational patterns and associated energies. it's energy levels are constained to certain values...it's degrees of freedom are limited.

Another helpful analogy is to think of the electron as a wave...when it's in free space the wave is everywhere, it extends all over the place. But when attracted by a proton in a nucleus, for example, that wave is now localized...it's constrained and so its different from the free space case. And the constraint is also modified by the presence of other electrons and additional protons. Since the energy is contained in the wave, changing it's configuration via the presence of nearby particles changes the wave characteristic and likely energy levels. It's very unlikely for the electron to be found between allowed energy levels.

In contrast, a free electron can take on any energy level. But when it is part of an atom or a larger structure, it's constrained...it's degrees of freedom are determined and limited by the whole structure. So an electron's energy levels and degrees of freedom are determined by the numbers of protons in the nucleus as as well as the particular structure of a lattice, as examples. The Schrodinger wave equation describes these.

 

[Naty1]

Why (or how) do refractive index of a medium differs for light with different frequencies?

because different frequencies have difference energies; These change the EM waves in the medium differently...

See this explanation:
http://en.wikipedia.org/wiki/Refractive_index#Microscopic_explanation

 

[andrien]

Why (or how) do refractive index of a medium differs for light with different frequencies?

there is quite a general formula for determining it.Since classical and quantum mechanics essentially gives same result for it.it is amusing to note that classical description involves electron bounded to atom by a restoring force to get the refractive index.

 

[110010]

Thank you all for the replies!