Simple Harmonic Oscillators: Visualizing Classic and Quantum

The first three modes of a classic simple harmonic oscillator appear in brief claymation animations. The blue ball goes from one end to the other, speeding up once, twice, or three times along the way. The quantum SHO has the ball appear randomly, but avoiding the same spots it rushed through in the classical animation. The superposition of the quantum states creates a vague impression consistent with the animations.

Category:

Science & Technology

Tags:

• Physics
• SHO
• Simple
• Harmonic
• Oscillator

[SubharmonicTheoretic]

I think for the second mode, it might be more accurate to indicate the wave's alternating velocity crests/troughs in terms of fifths (ie: decreases in velocity taking place at 2/5 and 4/5). But, I'm fairly new to these concepts and am a musician who has never taken a physics course so feel free correct that with a vengeance. Either way, I loved this video and found it very unique and useful. Thank you.

[sweetser]

@SubharmonicTheoretic On a guitar string, the start and end of the string are fixed and never move no matter how it is plucked. Math wonks call that a boundary condition. The fundamental mode of a short string is a higher pitch than a longer one.

Here is the series you suggest: 0/5 (the start), 2/5, 4/5, 5/5 (the end). The 0/5 and 5/5 must be there unless on of the ends of the strings is fee (like a wind instrument). 0/0, 1/3, 2/3, 3/3 sounds right, as does 0/5, 1/5, 2/5, 3/5, 4/5, 5/5.

[debunker1905]

So is this the explanation to the orbitals of electrons? Do electrons orbiting the nucleus behave just like quantum harmonic oscillators and the orbitals in this electronic clouds is just a superposition of all possible places the electron can be and the orbitals show the places where the electron is most likely to be found, that is, the maximum probability density, just like that "blueish" of the ball in your video. Am I correct, almost correct or else? Thank you.

[sweetser]

@debunker1905 The pattern of the electron is governed by a specific differential equation. I did not use that equation for this work. In a fuzzy way, I do think this is the way to think about electrons :-) I was happy the superposition appeared so darn faint since that is what experiments says of the atom. In a sense, you are correct, and I need to do more work.

[debunker1905]

@sweetser Oh, I see, and what is this specific differential equation, is it schrödinger's?

Your video was very good.

[sweetser]

@debunker1905 Yup, I would need a spin 1/2 solution to the Schrödinger wave equation.

Thanks, it was fun to make!

[CatsRuleDogsAreTards]

Its a blue Cylon eye.

[sweetser]

Hello Georgios:

If you took quantum mechanics today, they would not show this video. I have a non-standard way of looking at visualizing math in physics. For me complex numbers have time as the real, space as the imaginary component. That is not widely accepted. Yet time reflect looks different from space reflection (the first requires memory, the second a mirror).

It was one of the happy surprises of my life how faint the superposition in this video looks, still brings a smile.

[GeorgiosMICHALAKIS]

Fantastic! Too bad we didn't have this "back then" when I was learning physics!!

[ssnatcherss]

Hehe... Claymation = a poor man's computer model.