How does the wavefunction of an antiparticle differ from that of the particle?

Question

In this question I was answered that the invertion of wave function does not give antiparticles.

Then how does the wavefunction of an antiparticle look, given the wavefunction of the corresponding particle?

Answer 1

An antiparticle is a separate species and a separate particle. It has its own dimensions in the configuration space.

Suppose we have an electron and a positron. Denote electron's position as $\vec x_\mathrm{e^-}$ and positron's position as $\vec x_\mathrm{e^+}$. Then the wavefunction of the system will be a function of 6 coordinates (3 for each of $\vec x_\mathrm{e^\pm}$):

$$\psi(\vec x_\mathrm{e^-},\vec x_\mathrm{e^+}).$$

It won't be easy to plot such a function. If both particles are constrained to move in one dimension, the total wavefunction will be a function of two variables, which would be easier to plot. E.g. for a ground-state electron in an infinite square potential well and a twice-excited positron in the same well we'll have the following function:

If we only have an antiparticle, e.g. a positron, then the wavefunction will be generally of the same form as that of an electron. We won't know what particle it represents unless it's said somewhere in the text that defines it.