Some questions about Vibration and Quantum Physics(Pretty simple I think)

nukeman

Hey all!

Does vibration create a wave or a disturbance?

If I have something like a particle or something more massive like a molecule, and it vibrates, does it create a wave function?

If you have a stadium of people (yea I know, silly example) and one line of people start a wave or rather just move up and down ( you know like at sporting events you all start a wave of people), and this disturbance continues transverse to the direction of motion, yet nothing is moving except the people going up and down in their chair, and it all started from them moving up and down.

So, if I have a field, and at one end a particle vibrates, does that vibration create a disturbance in the field proportional to the frequency that the first particle vibrated at, ultimately affecting a particle at the other end of the field, or someplace within the field? ??

Drakkith

A wave is a disturbance.

Per wiki:
A wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves.

You don't create a wave function by performing a physical action, it is a mathematical tool we use and have to calculate it for every particle or system of particles.


Of course. This is how radio waves are created. Electrons are oscillated back and forth at the frequency you want to send at.

waveandmatter

The example in the end of your post, ie oscillating particles that are coupled to each other, are precisely what sound waves are. You can actually model them with coupled harmonic oscillators (or better with mass points with springs in between).

If you have a charged particle and wiggle it, you can also create electromagnetic waves. But this is a different example from the one with the sound waves, because the electromagnetic wave does not need a medium made of particles. It can affect other particles, but it can just as well propagate in vacuum.

In any case, these should not be confused with quantum mechanical wave functions! You can treat all the waves mentioned above quantum mechanically and you might even get something like a wavefunction (associated with a quasi-particle in the case with the sound waves and with a photon in the case with the electromagnetic waves), but those are not identical at all with the physically observable wave. I recommend book 1 of the 2 Cohen-Tannoudji books on QM to properly understand the mathematical and physical difference.

sophiecentaur

The problem with using the 'Mexican Wave' as an example of waves is that this wave is not a simple transfer of energy from place to place. It is being 'actively maintained' by the participants. It is true that, even if individuals actually obeyed the rule of starting to stand up only when their neighbour was up, then the 'standing up information' would be propagating as a wave but, unlike a water wave (and all the others), the Mexican Wave requires a constant input of new energy to make it propagate. However, the Maths describing its shape in time is the same.

nukeman

Hey thanks for explaining that better.

So if I have a particle, and it vibrates at a certain frequency, can you try and explain how this creates a wave, as in the physics of this type of wave created by a particle that vibrates at a certain frequency?

sophiecentaur

To get an idea of how waves work, I think it's best to consider a more classical model first (it's all the same in the end).

If you consider a line of masses, connected by springs (in space, to reduce the complications). If you disturb the mass at one end, it will pull on the first spring and the second mass will start to move but its motion will be delayed because of its mass and the finite stiffness of the first spring. The movement is transferred along the whole line of masses in the same way and, if the exitation is repeated at a steady rate, there will be a continuous wave, travelling along the line with the phase of the motion being more and more delayed as you look further along. The Energy is being transferred from one end to another of the chain.
All 'mechanical' waves work like this (sound / strings / seismic etc.). EM waves can travel without any meduim to support them but, instead of mechanical forces and displacements, the energy is carried by oscillating Electric and Magnetic fields. Exactly the same basic wave equations describe all sorts of wave, though.

'Your particle' will be creating a wave by passing its energy to a nearby particle, which will, in turn, pass it on to another particle etc. etc. just like the masses above. Needless to say, the energy involved with just one particle moving would be very small. Normally there will be a very large number of particles - as inside a lump of rubber or on a metal string and there will be more equivalent 'springs' involved.

nukeman

Ok ok, I see what you are saying.

I have 2 last questions hopefully you can help with, so I don't have to start another thread. Getting some fantastic info in here :)

1: Can you describe/explain the differences in a wave (like how you explained above), and a quantum wave function?

2: Lets say I have a particle(x) and its vibrating at a certain frequency. Now, the wave that is caused by that particle, can it bypass a medium (like a cellular membrane, or skin) and affect the vibrational frequency of a particle on the other side of this medium, lets called it particle(y). ?

sophiecentaur

You seem to be referring to the De Broglie idea that you can assign a wavelength to a particle with a wavelength which relates to its momentum. The wavelike nature of a particle (and it needs to be small, like a fundamental particle) sometimes reveals itself, like when an electron is bound to an atom. In that case, a wave solution gives a good description of how the atom can absorb or emit EM radiation. Also, electrons display a wavelike behaviour when you pass a beam of fast electrons through a regular lattice of metal atoms and you get a diffraction pattern. But this approach only works at the microscopic level. A cannon ball never displays a wavelike nature because it has too complicated a quantum state.

waveandmatter

To the first question:

A "physical" wave can be measured in terms of pressure (in the case of the example with springs or a sound wave in gas), or electrical fields / intensities (in the case of the EM field).

A QM wavefunction is actually a probability amplitude for the position (or other variables describing the state) of a particle. This means if you take the absolute square value of the wave function at any point in space this can be interpreted as the probability to find the particle there.
This also implies, that the wave function can _not_ be measured (it is not even a real, but a complex valued function). The only thing that you can get from (the average of) lots of measurements is the absolute square of the wave function, because a spatially resolved map of your particle counts will directly map to this abs square value.
The wavefunction itself does not exist physically, it is just a construct that tells you about probabilities.

nukeman

Both of you guys, Thanks!!

So, please tell me if this is correct.

If I have something much larger than a particle, lets say some type of hydrogen molecule (like heavy water or just water) That single molecule will have a vibrational frequency, thus creating a wave. This wave will travel to other molecules near by and if near to a medium, like a cell membrane, will ancounter that.

BUT, this is just a mechanical wave, and cannot be at all related to a quantum wave function, because when we are talking about quantum mechanical waves, we are dealing with MUCh smaller objects and functions.

So, you cannot apply quantum mechanics to a heavy water molecule correct?

Drakkith

It will only create a wave if the molecule has energy to impart into another particle. It doesn't make a wave simply because of it's existence.

Well, even single atoms have wave functions that are...complicated. The nucleus itself is very heavy and will have a very very small range of possible positions even in the simple example of hydrogen. Electrons, being about a thousand times lighter, are able to form large orbital clouds because of their small mass. But even atoms and molecules can be described by a wave function, it's just that the calculations are exceedingly complex and generally not able to be solved completely I believe. (So I've read)

Sure, you could do it. It's just that the calculations are extremely complex, and the size and mass of the atoms/molecules makes it much easier and almost as accurate to work classically in many cases.

nukeman

Gotcha! Thanks for the info. Looks like I am a little over my head in what I want to do :) My goal is to simply understand the characteristics of a WAVE that is created by a molecule that vibrates.

Interesting stuff tho :)

sophiecentaur

There are two issues here.
I think you are confusing a wave that is Created by a particle with the wave that can describe the Particle itself. Any particle can Vibrate and pass those vibrations on to another particle but that has nothing to do with de Broglie (afaik).

nukeman

I think you are 100% correct in that statement :(