The quantum harmonic oscillator

RiverLyle
 KVRer
 10 posts since 25 Jul, 2016
The quantum harmonic oscillator
The quantum harmonic oscillator
This name sounded great even for a DIY project of making a synth or a song even.
Source here (scroll down): https://en.wikipedia.org/wiki/Correspondence_principle
If anyone already got it share it! (or let us know where you bought it!)
This name sounded great even for a DIY project of making a synth or a song even.
Source here (scroll down): https://en.wikipedia.org/wiki/Correspondence_principle
If anyone already got it share it! (or let us know where you bought it!)

RiverLyle
 KVRer
 10 posts since 25 Jul, 2016
Re: The quantum harmonic oscillator
The quantum harmonic oscillator
Here is a demonstration[8] of how large quantum numbers can give rise to classical (continuous) behavior.
Consider the onedimensional quantum harmonic oscillator. Quantum mechanics tells us that the total (kinetic and potential) energy of the oscillator, E, has a set of discrete values,
{\displaystyle E=(n+1/2)\hbar \omega ,\ n=0,1,2,3,\dots ~,}E=(n+1/2)\hbar \omega ,\ n=0,1,2,3,\dots ~,
where ω is the angular frequency of the oscillator.
However, in a classical harmonic oscillator such as a lead ball attached to the end of a spring, we do not perceive any discreteness. Instead, the energy of such a macroscopic system appears to vary over a continuum of values. We can verify that our idea of macroscopic systems fall within the correspondence limit. The energy of the classical harmonic oscillator with amplitude A, is
{\displaystyle E={\frac {m\omega ^{2}A^{2}}{2}}.}E={\frac {m\omega ^{2}A^{2}}{2}}.
Thus, the quantum number has the value
{\displaystyle n={\frac {E}{\hbar \cdot \omega }}{\frac {1}{2}}={\frac {m\omega A^{2}}{2\hbar }}{\frac {1}{2}}}n={\frac {E}{\hbar \cdot \omega }}{\frac {1}{2}}={\frac {m\omega A^{2}}{2\hbar }}{\frac {1}{2}}
If we apply typical "humanscale" values m = 1kg, ω = 1 rad/s, and A = 1 m, then n ≈ 4.74×1033. This is a very large number, so the system is indeed in the correspondence limit.
It is simple to see why we perceive a continuum of energy in this limit. With ω = 1 rad/s, the difference between each energy level is ħω ≈ 1.05 × 10−34J, well below what we normally resolve for macroscopic systems. One then describes this system through an emergent classical limit.
Here is a demonstration[8] of how large quantum numbers can give rise to classical (continuous) behavior.
Consider the onedimensional quantum harmonic oscillator. Quantum mechanics tells us that the total (kinetic and potential) energy of the oscillator, E, has a set of discrete values,
{\displaystyle E=(n+1/2)\hbar \omega ,\ n=0,1,2,3,\dots ~,}E=(n+1/2)\hbar \omega ,\ n=0,1,2,3,\dots ~,
where ω is the angular frequency of the oscillator.
However, in a classical harmonic oscillator such as a lead ball attached to the end of a spring, we do not perceive any discreteness. Instead, the energy of such a macroscopic system appears to vary over a continuum of values. We can verify that our idea of macroscopic systems fall within the correspondence limit. The energy of the classical harmonic oscillator with amplitude A, is
{\displaystyle E={\frac {m\omega ^{2}A^{2}}{2}}.}E={\frac {m\omega ^{2}A^{2}}{2}}.
Thus, the quantum number has the value
{\displaystyle n={\frac {E}{\hbar \cdot \omega }}{\frac {1}{2}}={\frac {m\omega A^{2}}{2\hbar }}{\frac {1}{2}}}n={\frac {E}{\hbar \cdot \omega }}{\frac {1}{2}}={\frac {m\omega A^{2}}{2\hbar }}{\frac {1}{2}}
If we apply typical "humanscale" values m = 1kg, ω = 1 rad/s, and A = 1 m, then n ≈ 4.74×1033. This is a very large number, so the system is indeed in the correspondence limit.
It is simple to see why we perceive a continuum of energy in this limit. With ω = 1 rad/s, the difference between each energy level is ħω ≈ 1.05 × 10−34J, well below what we normally resolve for macroscopic systems. One then describes this system through an emergent classical limit.

resynthesis
 KVRist
 457 posts since 17 Sep, 2007 from Planet Thanet

Meffy
 Skunk Mod
 20866 posts since 10 Jun, 2004 from Pony Pasture
Re: The quantum harmonic oscillator
Maybe https://www.quicklatex.com/ ? Paste in your LaTeX code, click button, copy and paste the link they provide. You get a rendered image, they get a backlink.

whyterabbyt
 Beware the Quoth
 27856 posts since 4 Sep, 2001 from R'lyeh Oceanic Amusement Park and Funfair
Re: The quantum harmonic oscillator
Im not sure if its his LaTeX code, the entirety of his second post looks like its cut and paste from the Wiki article.Meffy wrote: ↑Thu Jan 23, 2020 7:23 pmMaybe https://www.quicklatex.com/ ? Paste in your LaTeX code, click button, copy and paste the link they provide. You get a rendered image, they get a backlink.
Im not sure how informed the user is about the subject, its a bit 'hey this is some thing that mentions oscillators, so SMOP, where do I get?'
"The bearer of this signature is a genuine and authorised pope."

BertKoor
 KVRAF
 11480 posts since 8 Mar, 2005 from Utrecht, Holland
Re: The quantum harmonic oscillator
How practical is it? It's probably limited to sine waves anyway.
Surely it oscillates, but can you change its frequency? How to get out a voltage of around 1V?
Does it need a cubic meter of equipment, consuming 15kW power?
So many questions, and no answer on wikipedia
Surely it oscillates, but can you change its frequency? How to get out a voltage of around 1V?
Does it need a cubic meter of equipment, consuming 15kW power?
So many questions, and no answer on wikipedia
We are the KVR collective. Resistance is futile. You will be assimilated.
My MusicCalc is back online!!
My MusicCalc is back online!!

vurt
 addled muppet weed
 58951 posts since 26 Jan, 2003 from through the looking glass
Re: The quantum harmonic oscillator
does it work like quantum computing?
im not sure drilling holes to alternate dimensions and bringing back extra resources, is advisable for music related projects.
the risks outweigh the benefits, better tuning/turning the universe inside out
im not sure drilling holes to alternate dimensions and bringing back extra resources, is advisable for music related projects.
the risks outweigh the benefits, better tuning/turning the universe inside out
look for the true freak label.
do not!feed the vampyr.
click link to hear the sounds of vurt coming into your ears
do not!feed the vampyr.
click link to hear the sounds of vurt coming into your ears

vurt
 addled muppet weed
 58951 posts since 26 Jan, 2003 from through the looking glass
Re: The quantum harmonic oscillator
but, send the wiki page to game changer fx in latvia, bet theyd have fun with it
look for the true freak label.
do not!feed the vampyr.
click link to hear the sounds of vurt coming into your ears
do not!feed the vampyr.
click link to hear the sounds of vurt coming into your ears

Meffy
 Skunk Mod
 20866 posts since 10 Jun, 2004 from Pony Pasture
Re: The quantum harmonic oscillator
Yes, the [8] was a bit of a giveaway. By "his" I meant whatever code he wants to render.whyterabbyt wrote: ↑Fri Jan 24, 2020 2:41 amIm not sure if its his LaTeX code, the entirety of his second post looks like its cut and paste from the Wiki article.
My standard reply to explicit declarations of SMOP is "Best hit the books. It'll be simple."

vurt
 addled muppet weed
 58951 posts since 26 Jan, 2003 from through the looking glass
Re: The quantum harmonic oscillator
not the same i know, but im currently using the cmb as an oscillator. would happily sell the secret for 1 million dollars!!!!
(cosmic microwave background)
(cosmic microwave background)
look for the true freak label.
do not!feed the vampyr.
click link to hear the sounds of vurt coming into your ears
do not!feed the vampyr.
click link to hear the sounds of vurt coming into your ears