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I am fascinated by many colour phenomena. When reading about several of them, I have come across all the explainations mentioned in the title. For example:

  • Conjugated Chains in molecules (specifically indicators): colour explained by particle in a box model (HOMO-LUMO transitions).

  • Colours of quantum dots vary with size of the particle, explained by quantum confinement.

  • Colour of gold colloids. Colour depends on particle size and shape,
    explained by surface phonon resonance frequency.

My understanding of all of these phenomena is limited, as I am not myself able to solve the Shroedinger equation, I simply try to understand the results. My understanding of the last two explainations is particularly poor.

I struggle to point out the difference in the different models. They all seem to explain electrons occupying a confined space, and the Shroedinger Equation solved with these constraints gives discrete energy levels. The absorption/emissions of photons due to electrons varying between these energy levels results in observed colour.

Edit: Can someone point out the essence in each of these models, in a way that the differences become clear?

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    $\begingroup$ So what exactly is the question? $\endgroup$
    – Mark Mitchison
    Commented Dec 4, 2016 at 11:13
  • $\begingroup$ @MarkMitchison I have now made an edit to make my question more clear. $\endgroup$
    – Adroit
    Commented Dec 4, 2016 at 13:12

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Colors are determined by the energy levels of the light absorbing or emitting systems.

Quantum dots are (semiconductor) structures which are comparable in size to the de Broglie wave length in the respective crystal. Depending on the finite size and shape (boundary conditions) of the quantum dots, you have standing electron waves in these quantum dots which correspond to a number of specific energy levels for the absorption and emission of light.

In gold particles similarly a number of energy levels for the absorption of light occurs due to standing surface plasmon-polariton waves. These waves consist of coupled oscillations of electron density and electromagnetic fields which can propagate along the interface of a metal with a negative real part of permittivity and a dielectric (air). On small gold particles, like spheres, these surface waves can form standing waves (not related to de Broglie waves) with discrete frequencies which are related to absorption frequencies of light and thus determine the color of these particles.

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  • $\begingroup$ Would it be right to say that the effects are similar, but varying in the scales they operate on? As in: Quantum confinement has to do with the wave movement of a single electron being constrained (width of particle approaching de Broglie wavelength of electron in orbit). Meanwhile plasmon oscillations are strings of electrons moving in waves, and the possible energy states are constrained by width. An analogy would be water waves vs the vibration of a single water molecule. Is there any major flaw in my description? Also, both of these explanations are classical, right? $\endgroup$
    – Adroit
    Commented Dec 4, 2016 at 16:21
  • $\begingroup$ You are right in your analogy! But in the end, also the classically derived surface plasmon oscillations are "quantized" by assigning energies $E=\hbar \omega$ to them. The quantum dot energies are derived by the solution of the Schroedinger wave equation in the confined quantum dot structure. $\endgroup$
    – freecharly
    Commented Dec 4, 2016 at 19:32
  • $\begingroup$ I see! So in the case of plasmon resonance we are dealing with standing waves. And standing waves can only exist at given frequencies for a given length of string. And the energy of these waves is given by the frequency by E=hv? Please correct me if I am wrong. So why are wavelengths of light with the same frequency as the standing wave preferentially absorbed? Does this increase the amplitude of the wave? $\endgroup$
    – Adroit
    Commented Dec 4, 2016 at 22:47
  • $\begingroup$ @Adroit - Here is a good review article on surface plasmons in nanoparticles which will probably give you the answers you are looking for: "Surface plasmons in metallic nanoparticles: fundamentals and applications", Garcia, M. A. JOURNAL OF PHYSICS D-APPLIED PHYSICS Volume: 44 Issue: 28 Article Number: 283001 Published: JUL 20 2011 $\endgroup$
    – freecharly
    Commented Dec 5, 2016 at 1:55

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