Wikipedia:Featured picture candidates/Quantum Harmonic Oscillator

Quantum harmonic oscillator: nomination for "featured diagram"

Voting period is over. Please don't add any new votes. Voting period ends on 17 May 2011 at 17:02:35 (UTC)

**Original** - Some trajectories of a harmonic oscillator (a ball attached to a spring) in classical mechanics (A-B) and quantum mechanics (C-H). In quantum mechanics, the position of the ball is represented by a wave (called the wavefunction), with real part shown in blue and imaginary part in red. Some of the trajectories, such as C,D,E,F, are standing waves (or "stationary states"). Each standing-wave frequency is proportional to a possible energy level of the oscillator. This "energy quantization" does not occur in classical physics, where the oscillator can have *any* energy.

Reason

this animation illustrates key concepts about the solutions of the time independent and time dependent Schrödinger equations better than anything I've ever seen before, and therefore has exceptional educational value. Specifically,

it is a good illustration of the complex nature of the solutions, implicitly explaining why the probability density of a stationary state is constant over time,
it shows the existence of non-stationary states for bound particles, which are often ignored in education but are key to a complete understanding of quantum mechanics
is demonstrates that a superposition of stationary states is not stationary
it illustrates how a coherent state resembles the classical description

The resolution is appropriate for embedding on wikipedia pages; see "Articles in which this image appears" below. Demanding a higher resolution would be unreasonable because

the current version is just below the 12.5-million-pixel limit for animations in wikipedia articles;
animated gifs cannot be scaled.

Also refer to the featured diagram File:Snells law wavefronts.gif, which is similar in technical and educational qualities.

Articles in which this image appears

Schrödinger equation, Stationary state, Quantum harmonic oscillator, Quantum mechanics

FP category for this image

Diagrams, drawings, and maps/Diagrams

Creator

Sbyrnes321

Support as nominator --OneAhead (talk) 17:02, 8 May 2011 (UTC)[reply]
I don't get it... Aaadddaaammm (talk) 16:22, 9 May 2011 (UTC)[reply]
Oppose -- I don't get it either. As far as I understand, A and B are physical illustrations of the oscillations while C-H are mathematical representations (that is what I understand from "real and imaginary parts"). If an image is worth 1000 words, this doesn't seem to be the case here... Alvesgaspar (talk) 17:28, 9 May 2011 (UTC)[reply]

It is contrasting classical physics (A and B) and quantum physics (C-H); they are all physically real but C-H occur at quantum scales and A and B occur at classical scales. Real and imaginary parts refers to the real (number) and imaginary number solutions to the time dependent Schrödinger equation, both of which are physically real and relavent to real life... - Zephyris _Talk 19:25, 9 May 2011 (UTC)[reply]

I understand that very often physicists use complex math for their models because it is a powerful tool. However there is a fundamental difference between the two sets: while the first illustrates the physical phenomenon, the second illustrates the mathematical model. I know very little about quantum physics but maybe there is a better way to graphically illustrate the standing quantum waves rather than with sinosoids. Alvesgaspar (talk) 20:30, 9 May 2011 (UTC)[reply]

The second doesn't illustrate a mathematical model, it really does show what actually happens in the quantum physical phenomenon. Unfortunately there probably is no way to illustrate a quantum wavefunction intuitively. - Zephyris _Talk 21:33, 9 May 2011 (UTC)[reply]

I agree - this figure is about as close as it gets to an intuitive illustration. OneAhead (talk) 15:42, 7 July 2011 (UTC)[reply]

@Alvesgaspar: for systems that are dominated by quantum effects (like covalent bond stretching in molecules), it's exactly the opposite: C-H represent physical reality, and A and B are simplified mathematical models which make it easier for the human mind to think about and for computers to calculate (Quantum Chemistry vs. Molecular Mechanics). OneAhead (talk) 15:42, 7 July 2011 (UTC)[reply]

Support This is a great representation of something extremely hard to explain, let alone illustrate. - Zephyris _Talk 19:25, 9 May 2011 (UTC)[reply]
Oppose To Zephyris, those aren't separate real and imaginary solutions - they are the real and imaginary components of a single complex solution. I agree that this is a subject very difficult to explain if the reader doesn't have a background in differential equations. For a reader without the appropriate background, the quantity $|\Psi |^{2}$ $|\Psi |^{2}$ is the important one. $|\Psi |^{2}$ $|\Psi |^{2}$ is a probability density function giving the "chance" that a particle is in a given place. Whilst the graphs have this information implicitly, it isn't really immediately visible as it should be for a simple explanation. For the reader with more background it is $\Psi$ $\Psi$ that is important (particularly with regard to the superposition of solutions) so you need both graphs. For such a reader I'd really like to see a lot more information about each solution (such as which eigenvalue each corresponds to). The information desired is probably implicit in the code. I'm also concerned that Quantum harmonic oscillator largely talks about the time independent Schrödinger equation, but this includes wave functions which are not solutions to that equation, but I have not read that article in detail. JJ Harrison (talk) 07:48, 10 May 2011 (UTC)[reply]
- The corresponding animation for the probability density is also on the "Stationary State" page; the current picture illustrates something different. Additionally, I don't agree that background in differential equations is required - some basic high school-level understanding of functions and complex math should suffice. Indeed, the whole point of this picture is to intuitively show how the solution to the time-dependent Schrödinger equation behaves, without requiring intimate familiarity with differential equations or analysis of complex time-dependent functions. As for the Quantum Harmonic Oscillator page, I agree that it is eligible for improvement, but that shouldn't affect a judgment call on the quality of a picture on the page. OneAhead (talk) 19:48, 5 July 2011 (UTC)[reply]

Not Promoted --Makeemlighter (talk) 02:23, 18 May 2011 (UTC)[reply]

Conclusion: not promoted because almost nobody understands quantum physics, and what fools are we to attempt to try to make people understand?! OneAhead (talk) 19:48, 5 July 2011 (UTC)[reply]