Quantum mechanics representations $x$, $p$, and not $(x,p)$?

Question

In Quantum Mechanics, generally speaking we work with space representation $\Psi(x)$ and/or the momentum representation $\Psi(p)$ of wavefunctions. Are there representations with mixing of $(x,p)$, i.e., is there any $\Psi(x,p)$ representation in Quantum Mechanics?

Answer 1

There is a representation/framework that includes both conjugate variables. It's called the Wigner Distribution and is a quasiprobability distribution. You may want to google it.