why are wavefunctions waves

[Andeh]

1 more question about wavefunctions.

 

I understand what wavefunctions are (for the most part), but I still don't understand why they are waves.

 

And yes, I know that the Schrodinger equation is a wave-equation...but is there any way for anyone to explain why wavefunctions are waves without bringing the schrodinger equation into this?

 

Thanks, this question has been bugging me for ages.

[questionposter]

They are waves because of some very complex property of the fabric of space that makes matter and energy behave in a way that follows concise mathematical motions.

[Andeh]

Thank you.

So that's the simplest explaination that there is? I suppose I'll have to learn the math then.

 

 

[michel123456]

1 more question about wavefunctions.

 

I understand what wavefunctions are (for the most part), but I still don't understand why they are waves.

 

And yes, I know that the Schrodinger equation is a wave-equation...but is there any way for anyone to explain why wavefunctions are waves without bringing the schrodinger equation into this?

 

Thanks, this question has been bugging me for ages.

 

As far as I know, the principle of Schroedinger was not to answer the question "why" but only the question "how". And if the answer of the 'how' question corresponds to measurements, that's enough. His answer to the 'how" question was (partly) his equation, no further explanation.

IOW nobody so far can answer your question. Or if someone can, I am all ears.

Edited December 28, 2011 by michel123456

[MigL]

Yes, you definitely should learn the math, it really isn't that difficult.

 

But you should be less concerned with why they are waves, a common state of many physical phenomena, and more concerned with 'what' is waving. Most waves we are familiar with are in a medium such as water, air,etc,or waves of something physical such as electric and magnetic fields. What is waving in Shroedinger's equation however is not really a physical wave, but is somewhat related to a probability wave since the square of the amplitude of the wave at any point, is the probability of finding the particle at that point.

 

So as you can see it isn't the math, its the concepts of QM which are difficult to wrap your head around.

[questionposter]

Yes, you definitely should learn the math, it really isn't that difficult.

 

But you should be less concerned with why they are waves, a common state of many physical phenomena, and more concerned with 'what' is waving. Most waves we are familiar with are in a medium such as water, air,etc,or waves of something physical such as electric and magnetic fields. What is waving in Shroedinger's equation however is not really a physical wave, but is somewhat related to a probability wave since the square of the amplitude of the wave at any point, is the probability of finding the particle at that point.

 

So as you can see it isn't the math, its the concepts of QM which are difficult to wrap your head around.

 

Isn't it just the particle itself waving? I mean it's waving like a fluid and then our perception of it get's truncated to observe only a point. An electron doesn't have a probability of being in multiple places at once, it is multiple places at once, and that's because it's wave math is basically like dropping a pebble in the water, only the waves don't die out because they don't go anywhere.

Edited December 29, 2011 by questionposter

[ajb]

Technically, wave functions are not waves: the Schrodinger equation is not the wave equation.

[MigL]

Well, let's see if i can give some examples, questionposer.

 

Consider the wave equation of an electron. Now a classical wave would be like a bucket with some water in it, if you agitate the water, waves spread out until they hit the siges of the bucket and are reflected.

The electron,o on the other hand, can do something that classical particles and waves cannot. It can 'tunnel' to the outside of a square potential well, and back in again, if it chooses to. We explain this by having the wave overlap the sides of the potential well so that part of it lies outside the well. Now it doesn't make sense to consider that outside part of the wave to be 'part' of an electron since we consider electrons fundamental point particles, and so indivisible. The only available choice is to relate the wave equation to a a probability.

 

A similiar situation arises in electron scattering off an obstacle. In this case the incident electron wave would produce, upon scattering, several larger ripples or wavelets. Again we cannot conclude that these ripples represent pieces of a broken-apart electron for the same reasons presented in the first example. Again we must conclude that these ripples are related to the differing probability of the incident electron being deflected in that direction.

 

I realise that the wave function and Shroedinger's equation are not the same, AJB, butit was overlooked for the sake of simplicity.

[ajb]

The important thing is that the solutions to the Schrodinger equation satisfy a linear superposition principle, just like more "standard waves". This is also why the solutions are also called state vectors and similar. You can add two solutions to get another and you can multiply a solution by a complex number and it remains a solution. Thus the collection of all solutions forms an infinite dimensional vector space over the complex numbers.

[MigL]

You've lost me AJB ( you gotta remember to dumb it down for us ) as I don't see what the fact that 'any combination or product of solutions is also a solution' has to do with it. Am I missing something ?

 

Also, why is a wave function not technically a wave ? It looks like a wave and can be expanded mathematically as a combination of waves. Do you mean its not a real actual wave or am I again missing something ?

[ajb]

You've lost me AJB ( you gotta remember to dumb it down for us ) as I don't see what the fact that 'any combination or product of solutions is also a solution' has to do with it. Am I missing something ?

 

If [math]\psi_{1}[/math] and [math]\psi_{2}[/math] are soultions to the Schrodinger equation, for some given potential etc. then [math] a\: \psi_{1} + b\: \psi_{2}[/math] is also a solution with [math]a,b[/math] being complex numbers.

 

That is the solutions have a very simple linear superposition. This is not the general case for all differential equations.

 

Also, why is a wave function not technically a wave ? It looks like a wave and can be expanded mathematically as a combination of waves. Do you mean its not a real actual wave or am I again missing something ?

 

Technically wave functions are not waves because waves are solutions of the wave equation. This is really the mathematical definition and somthing to be aware of, but should not distract you too much.

[Widdekind]

Erwin Schroedinger originally viewed a quanta's "Wave Function" as the physical entity, i.e. fundamental "particles" are not actually "really small billiard balls", but "cloud-like balls of quantum play-do", that can spread out, contract, be squeezed, push apart, etc.

[Qubit]

This is my first reply, so bear with me, etc! Hello there... To my understanding, wavefunctions are not waves but the probability that you will find a particle at a particular place.

[questionposter]

Technically, wave functions are not waves: the Schrodinger equation is not the wave equation.

 

Isn't a wave function describing the wave characteristics of a particle though?

[ajb]

Isn't a wave function describing the wave characteristics of a particle though?

 

Mine was only a very technical point based on strict definitions in mathematics.