What is the relationship between particles and waves in QED?

[Shreya]

Homework Statement

So i was learning some basic quantum Physics especially wave Particle Duality. And I wrote a paragraph about it. Here it is:

Relevant Equations

"Everything is a particle whose position is predicted by a mathematical wave. Light is not a wave but is packet of energy whose position is predicted by the wave.The same goes for an electron. Interference pattern is a probability distribution of where we are likely to find an electron. When you measure the position of an electron, you find find it at a specific location.But when you do that a lot of times you get an interference pattern."

I am not sure if this is right. Are there any misconceptions that you notice?
Please be kind to help.

 

[PeroK]

Homework Statement:: So i was learning some basic quantum Physics especially wave Particle Duality. And I wrote a paragraph about it. Here it is:
Relevant Equations::

"Everything is a particle whose position is predicted by a mathematical wave. Light is not a wave but is packet of energy whose position is predicted by the wave.The same goes for an electron. Interference pattern is a probability distribution of where we are likely to find an electron. When you measure the position of an electron, you find find it at a specific location.But when you do that a lot of times you get an interference pattern."

I am not sure if this is right. Are there any misconceptions that you notice?
Please be kind to help.

It's not really correct at all. A particle's dynamic properties (e.g. position and momentum) are described by a wave-function. You're missing the key concept that the wave-function does not describe where the particle is but (probabilistically) where you will find the particle if you measure its position.

Quantum interference is not at all as you have describe it.

 

[Shreya]

You're missing the key concept that the wave-function does not describe where the particle is but (probabilistically) where you will find the particle if you measure its position.

Actually, that's what I meant by 'predict'. Wrong terminology on my part.

Quantum interference is not at all as you have describe it.

I'm sorry but I haven't heard about quantum interference (What's it?). What I wrote was about the interference pattern in Young's double slit experiment done on electrons (or rather electron diffraction).

 

[PeroK]

I'm sorry but I haven't heard about quantum interference (What's it?). What I wrote was about the interference pattern in Young's double slit experiment done on electrons (or rather electron diffraction).

See here for example:

https://en.wikipedia.org/wiki/Wave_interference#Quantum_interference

 

[Shreya]

All I meant about quantum interference is that:
Once you measure the position of an electron, you get a point. And we you do that for a lot of electrons you get a probability distribution like the one below. The point I wanted to make was that electrons are particles (and are not spread in space) and the wavefunction is purely mathematical.

I also wanted to how does the photon picture correlate with the EM wave one?

 

[PeroK]

All I meant about quantum interference is that:
Once you measure the position of an electron, you get a point. And we you do that for a lot of electrons you get a probability distribution like the one below. The point I wanted to make was that electrons are particles (and are not spread in space) and the wavefunction is purely mathematical.

I also wanted to how does the photon picture correlate with the EM wave one?

You have a double-slit interference pattern that can be described by classical wave mechanics. Are you asking for the purely QM description?

There are already several threads about that on here.

The simplest description is that the slits act as a measurement of lateral position and by the uncertainty principle create an uncertainty in lateral momentum. This explains single slit diffraction. The Superposition of the two single slit wave functions causes the interference pattern.

In other words, uncertainty and probability replace classical wave diffraction.

Note that uncertainty by itself is not interference.

 

[Shreya]

The simplest description is that the slits act as a measurement of lateral position and by the uncertainty principle create an uncertainty in lateral momentum. This explains single slit diffraction. The Superposition of the two single slit wave functions causes the interference pattern.

That was really helpful. Thank you!
Could you please help me with the photon confusion too in post #5? @PeroK & @phystro?

 

[PeroK]

That was really helpful. Thank you!
Could you please help me with the photon confusion too in post #5? @PeroK & @phystro?

The behaviour of light is governed by QED ( Quantum Electrodynamics). There is an introductory book by Feynman about it. This describes how things like reflection, refraction and diffraction work in the QED model.