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Kartazion

Anharmonic Oscillator

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ground-state.png

 

Good morning

I see that the anharmonic oscillator is rare in quantum physics.
But I know that anhanamorcity interprets internuclear distance (Morse).

Is there another anharmonic role in quantum physics / mechanics?

 


 

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5 hours ago, Kartazion said:

ground-state.png

 

Good morning

I see that the anharmonic oscillator is rare in quantum physics.
But I know that anhanamorcity interprets internuclear distance (Morse).

Is there another anharmonic role in quantum physics / mechanics?

 



 

No it is not rare, it is just that the simple harmonic oscillator is a good enough approximation for most purposes.

 

Jeffrey Steinfeld discusses anharmonicity in spectroscopy in his  (advanced) book

Molecules and Radiation - An introduction to Modern Molecular Spectroscopy

Dover

Edited by studiot

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The radiation ? Good after I do not know if I had presented it correctly, but an expert told me here and with the oscillator "you need a new model for EM radiation, because that's not how it works."

Indeed I found that: http://farside.ph.utexas.edu/teaching/qmech/Quantum/node120.html


So I'm going to reverse my question. What cannot we calculate with the harmonic oscillator in quantum mechanics?

Thank you.

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 gravity ?

edit :

oops we haven't a theory of quantum gravity

Edited by stephaneww

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59 minutes ago, stephaneww said:

 gravity ?

edit :

oops we haven't a theory of quantum gravity

We have the Loop quantum gravity https://en.wikipedia.org/wiki/Loop_quantum_gravity or https://en.wikipedia.org/wiki/Quantum_gravity 

But I found that A_quantum_oscillator_that_could_explain_gravity (I don't know what it's Worth)

Edited by Kartazion

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47 minutes ago, Kartazion said:

unless I'm mistaken, they're incomplete or speculative for some part

47 minutes ago, Kartazion said:

But I found that A_quantum_oscillator_that_could_explain_gravity (I don't know what it's Worth)

Both Academia and viXra are not very reliable sources.

Edited by stephaneww

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8 minutes ago, stephaneww said:

unless I'm mistaken, they're incomplete or speculative for some part

Let’s say that if you manage to join relativistic gravity with quantum mechanics then it’s won. So yes it's wobbly but very ingenious for the LQG.

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if it's wobbly it's not pure science like QM or Relativity, it's still at the research stage for the moment

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loop quantum gravity avoids renormalization of gravity through the use of Wicks rotation. It is the divergences of gravity that prevents it from being properly quantized to have a proper quantum theory of gravity.

Edited by Mordred

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13 hours ago, Mordred said:

loop quantum gravity avoids renormalization of gravity through the use of Wicks rotation. 

It's a little bit hard to find something about the Wicks rotation in gravity. I saw a report with the path integral formulation. It's very technical.

However, with the Wicks rotation here, I found that : 

Wick rotation connects statistical mechanics to quantum mechanics by replacing inverse temperature 1/(kBT) with imaginary time it/ℏ. Consider a large collection of harmonic oscillators at temperature T. The relative probability of finding any given oscillator with energy E is ...

Now consider a single quantum harmonic oscillator in a superposition of basis states, evolving for a time t under a Hamiltonian H.

...

 

13 hours ago, Mordred said:

It is the divergences of gravity that prevents it from being properly quantized to have a proper quantum theory of gravity.

The divergences of gravity? The different operating techniques?

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You found a relevant link in so far as it's main gist. In LQG you use wicks rotation which can be described as a mirror image of the waveform to determine finite boundaries of a wave-function. Whether or not that wave-function is sinusoidal or not. This allows finite quantization's of the numerous degrees of freedom in one loop diagrams. See renormalization. The one loop corrections mentioned under the divergences section is what plagues gravity in regards to the mass term. In LQC the earlier versions applied wicks rotations for the various particle degrees of freedom of the Langrangian's  for the " effective action " for each field.

https://en.wikipedia.org/wiki/Renormalization

 further details on the Langrangian's of each field (strong, Higgs, EM weak and somewhat gravity (still needs work)) can be hound here. Action correlates coordinate displacement of a particle to a field in accordance with the conservation laws of the standard model. In order to do this is expresses ratios of change between relations between the kinetic energy of the particle and the potential of the fields in question.

The link is in the form of perturbation theory using the four momentum and the Klein Gordon and Dirac equations for Lorentz invariance.

with regards to temperature in you link, there is a correlation between temperature and particle number density of a blackbody temperature. For example using the Bose Einstein statistics or the Fermi Dirac. The former for Bosons, the latter for fermions, (mixed states uses the Maxwell Boltmann) one can calculate the number density of any elementary particle given the blackbody temperature. Being QM/QFT this incorporates the quantum harmonic oscillator (which applies to both particle and field).

The problem with gravity is that you end up with infinite one loop corrections to maintain various conservation laws.

Edited by Mordred

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I understand for the moment the Minkowski diagram and its metric starting from the principle where the tensor is composed of its four dimensions. Then follows the Lorentz invariance in relation to its transformations.
Next in its basic explanation, and more new to me, is renormalization, which determines a quantified finiteness at an infinite phase; indeed this is all the more true for a loop.
The Wick rotation remains vague for me, even if I understand its loop diagram cut in the y axis to insert a junction of the infinite loop.
However I still struggle to get used with the Lagrangian.


I will now take a winding path to better understand.

During quantum decoherence, is the ground state of a particle considered as a correlated state?
In other words, does the correlated matter come exclusively from the excited state of the atoms, or so also requires the ground state?

I am not saying that the system does not need the ground state, it is just during the wave function collapse or for the density matrix approach.

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Here this article will help with Wicks rotation.

https://www.google.com/url?sa=t&source=web&rct=j&url=https://cds.cern.ch/record/536859/files/0202018.pdf&ved=2ahUKEwicjZX258vmAhV9IDQIHVBBDK4QFjAEegQIBhAB&usg=AOvVaw0pRhVoMpCuLopChA28_OuC

I will have time to look at your other questions after work.

Edited by Mordred

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Lol welcome to tensors, gamma in the above is the gamma matrixes.

Those are used with the Dirac and Wheyl spinors. 

Here is decoherence make sure you look at quantum coherence hyperlink. I will have more time later to help

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Correction to the above gamma is as per GR not gamma matrix. Misread it.

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4 hours ago, Mordred said:

Here is decoherence make sure you look at quantum coherence hyperlink. I will have more time later to help

I expected the wave function to disappear, to an excited atomic state. But apparently it's just a matter of interference.

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I don't know if it has to do with quantum decoherence, but I also saw this link: https://en.wikipedia.org/wiki/Coherent_states

In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state which has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator.

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Yes that link refers to quantum decoherence. Little hint anytime you see a reference to creation or annihilation operators your either dealing with QM or QFT.

You may find it handy to look up the Bra and ket notations (Dirac notation) 

To get a better grasp of the mathematics on that link.

Edited by Mordred

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12 minutes ago, Mordred said:

Yes that link refers to quantum decoherence...

So the connection between quantum decoherence and coherent states it would be with Schrödinger's equation...

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Correct for QM, for QFT the Klien Gordon. +1 for studyi

Edited by Mordred

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That theory lost popularity among the scientific community long ago. In essence symmetry gauge theory covers all the aspects of the above without specifying a single particle at all spacetime locations.

Now under QFT the particle number density varies accordingly to the field strength.

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I have to understand what a symmetry group is.
 

Here are some links I found. For some, it is difficult to get the paper.

- The complete symmetry group of a forced harmonic oscillator

- Symmetry groups and conserved quantities for the harmonic oscillator

- The symmetry group of the harmonic oscillator and its reduction

- U3 symmetry and clustering in the harmonic oscillator shell model

9 hours ago, Mordred said:

Now under QFT the particle number density varies accordingly to the field strength.

Density is determined only if the particles are correlated / observed. Otherwise you have to stick to the probability of the wave function, only.

No?

It's why Albert Einstein said: "I like to think the Moon is there even if I am not looking at it."

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