Why wavefunction is not seen as substance distribution?

Why wavefunction (the square of its modulus) of an electron is not seen as a measure of substance/charge distribution of the electron?

Nugatory
Mentor
That model only works if you're looking at the wave function of a single particle written in the position basis. In that case and only in that case will the wave function take the form ##\psi(x,t)## so that you can interpret it as the distribution of some substance at position ##x## and time ##t##.

Thus, it's a dead end - you'll abandon it for the more general mathematical formalism before you're half-way through your first QM textbook.

blue_leaf77 and bhobba
If you see it as a substance you get maybe the problem of measurement it should shrink to at least a peak when you measure position.
I suppose in copenhagen it is the knowledge about the position.

We have the same problem in classical mechanics : imagine you rotate your coordonate system then the coordinates of all objects change as far as infinity. No computer could do this instantaneously.

stevendaryl
Staff Emeritus
Why wavefunction (the square of its modulus) of an electron is not seen as a measure of substance/charge distribution of the electron?
The problem with thinking of the wavefunction as a physical quantity, or field, is that it doesn't exist in space, it exists in configuration space.

What I mean by that is this: Suppose we have two particles. The wave function for that pair is a function of the form:

$\Psi(x_1, y_1, z_1, x_2, y_2, z_2)$

which gives the probability amplitude for finding the first particle at $(x_1, y_1, z_1)$ and the second particle at $(x_2, y_2, z_2)$.

When you square it, you don't get the probability of finding anything at $(x_1, y_1, z_1)$, or of finding anything at $(x_2, y_2, z_2)$. You get the probability of simultaneously finding one particle at one location and the other particle at the other location.

vanhees71 and Demystifier
The problem with thinking of the wavefunction as a physical quantity, or field, is that it doesn't exist in space, it exists in configuration space.

What I mean by that is this: Suppose we have two particles. The wave function for that pair is a function of the form:

$\Psi(x_1, y_1, z_1, x_2, y_2, z_2)$

which gives the probability amplitude for finding the first particle at $(x_1, y_1, z_1)$ and the second particle at $(x_2, y_2, z_2)$.

When you square it, you don't get the probability of finding anything at $(x_1, y_1, z_1)$, or of finding anything at $(x_2, y_2, z_2)$. You get the probability of simultaneously finding one particle at one location and the other particle at the other location.
This makes very good sense. But it assumes that the wave functions (WFs) of the two particles cannot be separated. The general validity of this assumption should be by itself related to the subject question. On the other hand, when the two particles' wave functions can be separated, the overall wavefunction of the two, as a product of individual WFs (or a summation of such products), would be more or less artificial, and the proposed understanding of that WF of each particile be seen as the substance distribution of that particle can still make sense.

stevendaryl
Staff Emeritus