Particle Function? Particle Equation?

[MevsEinstein]

TL;DR

If there is a wave function, is there also a particle function? And what is the particle form of the wave equation?

The following is the wave equation from Electrodynamics: $$\frac{\partial^2 \Psi}{\partial t^2} = c^2\frac{\partial^2 \Psi}{\partial x^2}$$ Where $\Psi$ is the wave function. But because of Heisenberg's Uncertainty, physicists had to come up with another equation (the Schrödinger equation), which is "derived" from the wave equation.

But what about particles? Is there a particle function (opposed to the wave function)? And is there a Particle Equation? If not, why don't they exist? It is a very obvious thought.

 

[PeterDonis]

because of Heisenberg's Uncertainty, physicists had to come up with another equation (the Schrödinger equation), which is "derived" from the wave equation.

No, it isn't. The "wave equation for electrodynamics" that you gave is for classical electromagnetic waves. The Schrödinger equation is for quantum wave functions. They are two different things.

Is there a particle function (opposed to the wave function)?

No. Why would you expect there to be? Even on the basis of your claimed analogy with electrodynamics, this doesn't make sense; there is no "particle function" for electromagnetic fields.

 

[MevsEinstein]

No, it isn't. The "wave equation for electrodynamics" that you gave is for classical electromagnetic waves. The Schrödinger equation is for quantum wave functions. They are two different things.

That's why I put derived in quotation marks. The Schrödinger equation is motivated by the wave equation.

there is no "particle function" for electromagnetic fields.

I didn't limit particle functions to electromagnetic fields. I am just talking in general.

 

[malawi_glenn]

Summary: If there is a wave function, is there also a particle function? And what is the particle form of the wave equation?

But because of Heisenberg's Uncertainty, physicists had to come up with another equation (the Schrödinger equation

Its the other way around, you derive the uncertainty relation from wavefunctions.

Schrödinger equation was postulated 1925, the uncertainty relation in 1927

The uncertainty relation is a feature of signals in general

It is also quite misunderstood, it is a statistical statement.
Consider the standard deviation of an hermitian operator $\hat{\mathcal{A}}$, the standard deviation (squared) is defined as $\sigma_\mathcal{A}^2 = \langle \hat{\mathcal{A}} \hat{\mathcal{A}} \rangle - \langle \hat{\mathcal{A}} \rangle \langle\hat{\mathcal{A}} \rangle$
it is clear that the Heisenberg relation deals with expactation values of operators, it does not specifiy what ΔxΔp is for a single outcome.

 

[weirdoguy]

I am just talking in general.

Can you give us an example of "particle function"?

 

[Delta2]

Well the Schrödinger equation is some sort of a "mix" of particle equation and wave equation. According to the Copenhagen interpretation of wave function the square of the modulus of the wave function which is the solution to the SE, give us the probability that a quantum mechanical particle will be located at the point of space where the wave function was evaluated.

The only other thing I can think of is Newton's 2nd law in classical mechanics, where $$F=m\frac{d^2\mathbf{r}}{dt^2}$$ might be your so called "particle equation", it says that the second derivative of the position vector $\mathbf{r}$ of the particle times the particle's mass is equal to the total force exerted on the particle.

 

[PeterDonis]

The Schrödinger equation is motivated by the wave equation.

Not really. It was motivated by the idea of waves associated with quantum systems (as in de Broglie's idea), but not by the usual wave equation, since the dispersion relation Schrödinger used was not the one associated with the usual wave equation.

I didn't limit particle functions to electromagnetic fields. I am just talking in general.

The only analogy you gave was to the electromagnetic case. In the absence of some connection to known physics, or at least of some kind of response to the question I asked (the "why would you expect there to be?" question), "just talking in general" basically amounts to personal speculation, which is off limits here.

 

[PeroK]

Summary: If there is a wave function, is there also a particle function? And what is the particle form of the wave equation?

The following is the wave equation from Electrodynamics: $$\frac{\partial^2 \Psi}{\partial t^2} = c^2\frac{\partial^2 \Psi}{\partial x^2}$$ Where $\Psi$ is the wave function. But because of Heisenberg's Uncertainty, physicists had to come up with another equation (the Schrödinger equation), which is "derived" from the wave equation.

But what about particles? Is there a particle function (opposed to the wave function)? And is there a Particle Equation? If not, why don't they exist? It is a very obvious thought.

I'll try to guess the motivation for your question:

When a particle behaves like a wave, it obeys the Schrödinger equation. But, when a particle behaves like a particle, which equation does it obey?

 

[MevsEinstein]

Not really

I think I got scammed, Dr. Borge Gobel on his Quantum Physcis Udemy course said that the wave equation couldn't be used because of Heisenberg's uncertainty and that quantum physicists had to come up with a new equation. I was kind of confused with this, but I decided to just go with it.

The only analogy you gave was to the electromagnetic case.

Some people write introductions in their question, so I thought 'why not do the same thing'? I should've made a section and give it a title.

 

[MevsEinstein]

Can you give us an example of "particle function"?

Oh wait, finding the particle function of a wave doesn't make sense. I was thinking of the opposite of the wave function, but when I searched up what it exactly measures (since I only learned the mathematical definition), I realized we couldn't make a counterpart.

 

[MevsEinstein]

I'll try to guess the motivation for your question:

When a particle behaves like a wave, it obeys the Schrödinger equation. But, when a particle behaves like a particle, which equation does it obey?

When a wave behaves like a particle, but you just made me curious more by the question you wrote.

 

[PeterDonis]

Dr. Borge Gobel on his Quantum Physcis Udemy course said that the wave equation couldn't be used because of Heisenberg's uncertainty and that quantum physicists had to come up with a new equation.

Do you have a link?

 

[PeroK]

When a wave behaves like a particle, but you just made me curious more by the question you wrote.

Okay, perhaps I didn't understand your question after all.

 

[Delta2]

Oh wait, finding the particle function of a wave doesn't make sense

Well I am not sure what exactly you mean by that but I think this is called quantization of the field in Quantum Field Theory. This is how particles like photons arise from a quantization of electromagnetic field.

 

[malawi_glenn]

When a wave behaves like a particle

What kind of wave? What does "behave like a particle" mean?

 

[MevsEinstein]

Do you have a link?

https://www.udemy.com/course/quantumphysics/?src=sac&kw=quantum+physics But it's for money. Maybe I misunderstood, I will watch the lecture (motivating the Schrödinger equation) again to clarify.

 

[MevsEinstein]

Okay I watched it again and he said that the classical wave equation only works for waves and physicists wanted to find an equation that works for both waves and particles. They wanted this new equation to have the same solution as the classical wave equation that works for particle properties as well.

In another lecture he said the classical wave equation doesn't follow the Heisenberg uncertainty because of something that has to do with the second partial derivative with respect to time. I was kind of confused by this but I decided to just keep listening

 

[PeterDonis]

Okay I watched it again and he said that the classical wave equation only works for waves and physicists wanted to find an equation that works for both waves and particles. They wanted this new equation to have the same solution as the classical wave equation that works for particle properties as well.

In another lecture he said the classical wave equation doesn't follow the Heisenberg uncertainty because of something that has to do with the second partial derivative with respect to time. I was kind of confused by this but I decided to just keep listening

All of this indicates to me that these lectures are not very good at helping people to understand the actual physics involved. Unfortunately since you say you have to pay to watch them I'm not going to be able to give a more detailed critique since I have no intention of paying to watch them given what you have said so far.

 

[PeterDonis]

it's for money.

Btw, MIT OpenCourseWare is free:

https://ocw.mit.edu/

I would at least consider looking at this material before paying for something that, at the very least, does not have the same reputation for quality that a world-class university like MIT does.

 

[MevsEinstein]

All of this indicates to me that these lectures are not very good at helping people to understand the actual physics involved. Unfortunately since you say you have to pay to watch them I'm not going to be able to give a more detailed critique since I have no intention of paying to watch them given what you have said so far.

I feel so sad my life savings have been wasted

 

[MevsEinstein]

Btw, MIT OpenCourseWare is free:

https://ocw.mit.edu/

TYSM I can safely become a genius now

 

[Delta2]

TYSM I can safely become a genius now

Yes and conquer the universe too! :D