# This is a nonsensical question about wavefunctions

'If particles also behave as waves, then what is oscillating?'
I'm fairly sure that most people would consider this a nonsensical question. But I'm not sure why and I was hoping someone could clear this up for me.

My thoughts are:
The wave function is just a mathematical model, so don't panic.
Particles behave as waves as well, stuff isn't really either, it could really be something in between but nobody knows, so don't panic.

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What's oscillating is a particle field.

Obvious stupid question: what is a particle field?

'If particles also behave as waves, then what is oscillating?'
I'm fairly sure that most people would consider this a nonsensical question. But I'm not sure why and I was hoping someone could clear this up for me.

My thoughts are:
The wave function is just a mathematical model, so don't panic.
Particles behave as waves as well, stuff isn't really either, it could really be something in between but nobody knows, so don't panic.

Do you mean "what does it mean for ψ to oscillate in space?" This means the probability of finding the particle changes as you move through space at a given instant in time. The particle is more likely to be in some areas than others.

Do you mean "what does it mean for ψ to oscillate in time"? This means that, in a given region of space, the probability of finding the particle in that region changes over time (becoming more likely and then less likely and back again if the oscillation is sinusoidal).

This is a rather bare-bones explanation, and you need to be careful about you mean by "probability," but I think it conveys the basic answer to your question.

As Dirac_Man said, the wave function is basically a "probability wave".

Ah I think I get it. So no substance oscillates, but it's just a changing probability.

What I really meant by the question was not what is meant by ψ oscillating. But rather what is ψ? I get that it's a complex function which varies, varying probability amplitude etc. But what I mean to ask is if ψ is a wave-like function, describing a particle, then what is vibrating? Like you could describe a sound wave mathematically as some function, but the stuff that's oscillating is the air or whatever. So if a particle is also a wave, what is oscillating? Or rather, is it a nonsensical question to ask 'what is oscillating' in this context and that I should just shut up.

vanhees71
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The wave function is the representation of a quantum wrt. to the position observable, i.e.,

$$\psi(t,\vec{x})=\langle \vec{x} | \psi,t \rangle,$$

where I've used the Schrödinger picture of time evolution. Operators that represent observables are time independent, the state vectors time dependent in this picture.

According to the minimal statistical interpretation, $\psi(t,\vec{x})$ is not identified with a physical quantity but has the one and only meaning to be the probability amplitude for the particle's position.

This means, it describes the probability to find, at time $t$ a particle in a little volume element $\mathrm{d}^3 \vec{x}$ around the position $\vec{x}$, given the particle is perpared in the (pure) state, represented by the state vector $|\psi,t \rangle$, i.e., the probability distribution of the particle's position is given by Born's rule,

$$P(t,\vec{x})=|\psi(t,\vec{x})|^2.$$

This "minimal interpretation" is of course subject of big debate, and I'm pretty sure, we'll have another one in this thread soon. On the other hand it is the one, which is sufficient to interpret the mathematical formalism of quantum theory to real experiments in the lab and at the same time the one that introduces the least assumptions on its meaning with the least possibility of leading to contradictions with other fundamental principles of physics, as causality and locality that are very successful in describing elementary particles in terms of (relativistic) quantum field theory.