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Cuchulainn
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### Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

A friend of mine who is a geologist. He has questions and I thought some Wilmotters can shine their light on the problem. Thanks for your help..

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Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.
I believe that there is a bi-polar magnetic flip by the electron as it returns from its excited state to original position. The electron is admitting protons from stored energy as it does this 'flip'
The absorption, storing and readmitting of energy, albeit at a different wavelength, interests me.
I guess that it's the 'storage of energy' that should be of real interest here??
Danny you asked me to provide one question to be broken into mathematics ...
might have to be two questions which will need two answers each..one in maths, one in english
The word 'Forbidden' is what interests me in the above statement.

FIRST QUESTION:
Which theory is being broken for the energy state to become 'forbidden'?
and also
SECOND QUESTION:
Could  you explain the quantum mechanics required for the storage of this 'forbidden energy' in the phosphorescence of crystalline minerals please?

Cuchulainn
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### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

The exhibits

katastrofa
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### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

I wonder which Wilmotters (plural) will shine their light on the physics problem. I'll wait and see *grabs a carrot*

Cuchulainn
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### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

Actually, I was thinking about you as "prima inter pares". You can probably do it before lunch

Alan
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### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

Here's a couple educational-style references.
Spectroscopic selection rules
Phosphorescence

The chart in the second reference shows the story is rather complicated and I don't pretend to understand the details of it. But, the key paragraph there to answering the questions is:

"Both the singlet-triplet and triplet-singlet transitions violate the $\Delta S = 0$ selection rule. This rule applies absolutely only for pure electric dipole transitions, so the glow-in-the-dark T-shirts don't violate the laws of universe. Still, transitions that violate it are apt to be slow."

So, what is "forbidden" is an electron transition under a selection rule, which is only an approximation to what electron transitions are allowed. In particular, the most common types of photons are "electric dipole type". If these were the only ones, the transition under discussion could never happen. But they aren't -- so the forbidden transitions happen, but at a slow rate. There is elaboration in the upper right of the last page of first link. So, the theory that is being "broken" is a simplified account of atoms and radiation under which everything is non-relativistic and photons being emitted/absorbed are "electric dipole type" only. (Under a more sophisticated theory, called QED, these transitions are not forbidden, but are still "slow").

It's been a long time since I had quantum mechanics, so hopefully I am not totally misrepresenting things.

katastrofa
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### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

OPHELIA
My lord, he hath importuned me with love
In honourable fashion.
LORD POLONIUS
Ay, fashion you may call it; go to, go to.
OPHELIA
And hath given countenance to his speech, my lord,
With almost all the holy vows of heaven.
LORD POLONIUS
Ay, springes to catch woodcocks. I do know,
When the blood burns, how prodigal the soul
Lends the tongue vows: these blazes, daughter,
Giving more light than heat, extinct in both,
Even in their promise, as it is a-making,
You must not take for fire.
Shakespeare was so right about luminescence...
I once wrote analytical software for luminescence spectra for some guy from an Australian lab as one of my BSc projects. It used neural networks and had a GUI! Judging from the form of the questions, your friend needs some more basic intro. I'm too tired today (or is it tomorrow already?) - I'll be back tomorrow (or tomorrow's tomorrow).

Collector
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Joined: August 21st, 2001, 12:37 pm

### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

"Shakespeare was so right about luminescence..."

well Shakespeare was written by Bacon (& Co?)!  And no surprise Bacon was right, he walked into the right circles of knowledge... (hemm "but the Wilmot research has been exposed as a forgery" Baconian wiki)

which bring us to QED ?

Cuchulainn
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### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

For the record for our geological friends

Alan is physicist
katastrofa as well
Collect is a trader turned physicist
Cuchulainn is a numerical analyst

katastrofa
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### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

I'm a former physicist, now statistician. You are the Einsteins and Feynmans of Wall Street. The creators of the most effective money making formula: buy low, sell high (some of you got this part wrong), get bailed out.

Alan
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### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

Just ran across this nice history piece about the discovery of spin, which cites this nice interview with George Uhlenbeck

As Feynman famously said,  "I think I can safely say that nobody understands quantum mechanics".

Historically, all the rules/theory got nailed down and everybody agrees to them now (because they explained all this spectral fine structure, for one thing), but they remain somewhat of a mystery.

So, if the geologist friend is still awaiting a really intuitive explanation -- probably won't happen.

trackstar
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### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

Nice series of lectures on MIT OCW. This group from 2016 is really good.

It's MIT Quantum Physics I 8.04

If you open this in youtube, on the side bar, you will find links to each lecture in the full series.  Your friend might like Lecture 16 in general and 16.3, 16.5, and 16.6 in particular.

They cover energy below the barrier and a particle in the forbidden region.

It's a start, anyway.

Collector
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### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

Localized transition models in luminescence: A reappraisal

"transition model are solved analytically using the Lambert W function"

katastrofa
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### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

Feynman didn't understand many things, judging from all the errors in his Lectures. All "spooky" quantum effects are nothing else but statistics and only people who don't know statistics thoroughly enough (which applies to the majority of scientists) claim otherwise.

No laws of physics are broken in photoluminescence. When one finds that the laws of physics are broken, in 99.99% of cases it means that they do something wrong (e.g. don't take into account all important factors), in 0.01% of cases that they discover something new and in 0% cases that they are Collector. And when people give you meaningless percentage estimations, they are from finance - I'm just mocking you

The selection rules dictate which electron transitions are "allowed" and which are "forbidden". The rules result from the properties of wave function of states betweeh which the transitions are being considered. You calculate a so called transition momentum integral which is basically the probability of such a transition. Theoretically this probability is zero is when the states have different multiplicity, i.e. the transition would require changing the spin of electron - it's simply energetically unfavourable. However, the complete energetic calculation should include a lot of effects other than the properties of the single electron states, e.g. spin-orbit interaction, many-body interactions between the molecule atoms and electrons, etc. (just like there are some exceptions to Hund's rules in the periodic system of elements). The corrections are usually second order, but can induce a non-zero probability of the "forbidden" transition. Phosphorescence is due to such a "correction", and it's usually mainly the spin-orbit interaction (which is due to the specific features of the crystal symmetry) - what happens is the change in spin angular momentum compensates for the change in orbital angular momentum due to the transition. The unusually long phosphorescence duration (the materials can shine for hours) is related to the fact that the probability of this "forbidden" transition is very small (the correction is a higher order effect and generates just a very small transition momentum/probability - the electron "leaks" is density very slowly from its initial state to the final state).

It's actually chemistry, not physics. Quantum chemistry. I completed a BSc course in chemistry and even planned of continuing in this particular specialisation. It was many years ago, but the above problem is quite basics.

(Keywords in bold)
Last edited by katastrofa on August 23rd, 2018, 2:19 pm, edited 1 time in total.

Cuchulainn
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### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

It's actually chemistry, not physics. Quantum chemistry. I completed a BSc course in chemistry and even planned of continuing in this particular specialisation. It was many years ago, but the above problem is quite basics.

OK, if it is undergrad level, surely there must be a book discussing the topic?
The posts are very wordy... why no equation?

ppauper
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### Re: Forbidden energy states in the quantum mechanics of phosphorescent crystalline minerals.

what's with quantum mechanics in geology anyway?
what happened to "rocks for jocks?"