Basic - Trying to understand a probability wave

[FrogPad]

I'm having a hard time understanding the concept of a probability wave. Let me try to explain myself.

Imagine there is radiation propagating through free space. It has an electric field and a magnetic field oscillating orthogonal to one another as given by Maxwell's equations. It propagates at speed c. Thus I can actually visualize the wave traveling through space at speed c. I could actually get in front of this wave if I could travel faster than c (obviously I can't, I'm not arguing anything close to different...solely saying this for arguments sake). Now if other waves are in free space they will interfere with my wave that is traveling. If this wave goes through a tiny slit it diffracts.

Now what to do with the probability wave?

If I fire an electron through space. I can visualize this particle traveling at some speed. So do I now think of this electron also as a wave? Can I say that look here is a wave traveling through space. But it doesn't have a propagation speed right? I couldn't get in front of it. This is a probability wave, well what does that mean physically. When I take the modulus and square it I get a probability distribution of where this electron exists within a volume. How do I make the distinction between an EM wave and a probability wave?

A huge confusion comes in when we talk about the double slit experiment.

So a probability wave comes through slit one, and a another wave comes through slit two. They interfere with each other and change the probability distribution. So do I visualize these probability waves just like EM waves traveling through the slits?

Any help clarifying these rather elementary quantum ideas would be great. Thank you.

 

[azntoon]

The key difference between an EM wave and a probability wave is that the former is a classical wave that can be visualized, while the latter is a quantum wave that cannot be visualized. The probability wave describes the probability of finding a particle at any given point in space. In the double slit experiment, the probability waves from both slits interfere with each other to create an interference pattern, which is essentially the combined probability of finding a particle at any given point. Visualizing this process is difficult because the probability wave is abstract and cannot be seen.

 

[denian]

I can understand your confusion about probability waves. It is a fundamental concept in quantum mechanics and can be difficult to grasp at first. Let me try to explain it in a simple way.

First, it is important to understand that in quantum mechanics, particles can exhibit both wave-like and particle-like behavior. This is known as wave-particle duality. So, while we can visualize particles like electrons as traveling at a certain speed, they also have a wave-like nature.

Now, let's talk about the probability wave. In quantum mechanics, the state of a particle is described by a mathematical function called a wave function. This wave function contains all the information about the particle, including its position, momentum, and energy. When we square the modulus of the wave function, we get the probability of finding the particle at a particular position.

So, when you fire an electron through space, you can think of it as a probability wave. This means that the electron exists simultaneously at all points along the wave, but with varying probabilities. It is not a physical wave like electromagnetic waves, but rather a mathematical representation of the particle's state.

In the double slit experiment, the probability wave of the electron passes through both slits and interferes with itself, creating a pattern on the screen. This is because the probability wave is a superposition of all possible paths the electron could take. It is not like an electromagnetic wave that can be split into two separate waves.

I hope this helps clarify the concept of probability waves for you. It is important to note that these are just simplified explanations and the full understanding of quantum mechanics requires a deeper understanding of the mathematical formalism. Keep exploring and asking questions, as quantum mechanics is a fascinating and complex field.