What is the wave function for the whole system/atom ?

[Quandemonitum]

For example, let's say that psi(q) is the wave function of an electron(which describes/represents the electron) that is located in an atom and isolated/unentangled from the rest of the system. What is the wave function value of this psi(q) ? What is the wave function for that whole atom(with only one electron=hydrogen-like atom) ? What is the wave function for the whole atom[with more than one electron=multi-electron atom(other isolated electrons are represented by other wave functions such as psi(w), psi(t), psi(j), psi(v) etc.)](entanglement is not created!) What is the wave function for the whole atom[with more than one electron=multi-electron atom(other isolated electrons are represented by other wave functions such as psi(w), psi(t), psi(j), psi(v) etc.)](entanglement is created spontaneously so we can not talk about the listed wave functions above we have only one wave function that describes the quantum system/atom!=entanglement is created!)

(Attention1: Due to the entanglement principle, since there is an entanglement in multi-electron systems we can not talk about the separate wave functions that describe/represents other electrons, there is only one wave function that describes the whole system.)
(Attention2: Mathematical and physical proofs are required!)

 

[Nugatory]

(Attention2: Mathematical and physical proofs are required!)

If you want mathematical and physical proofs, you'll have to spend a few months with a decent introductory QM text - a thread in an online forum is no substitute. You'll find some recommendations for good textbooks elsewhere on this forum.

However, from some of your other questions, I suspect that you're asking a much more basic question: "What is all this stuff about wave functions and entanglements?". If so...

In general the wave function is $\psi(u1_x,u1_y,u1_z,u2_x,u2_y,u2_z, u3_x, ...)$ where the $u1$ values are the x, y, and z coordinates of the first particle, the $u2$ values are the x, y, and z coordinates of the second particle, and so forth. If we're considering just a single electron moving in one direction, then this simplifies down to the form that you've seen, $\psi(x)$, because we only have one particle and its position is described by the single number $x$. For a two-particle system in which both particles are constrained to move along the same straight line, we would write $\psi(x1,x2)$.

The function $\psi(...)$ is itself a solution to a differential equation called Schrödinger's equation. If $\psi(...)$ takes on a certain form ("non-factorizable" in the lingo) then we say that the particles covered by $\psi(...)$ are "entangled".

Beyond that... as I said, you have to find a decent textbook and get started learning (although the first thing you'll learn is that you have to learn some more math before you can get started).

This thread is closed.

 

[Quandemonitum]

Thank you. However i have one more question: what is the wave function for the whole hydrogen-like atom ? What is the association of this wave function with atomic orbitals in hydrogen atom ? Is that wave function for the whole atom equal to the linear combinations of the atomic orbitals in that hydrogen atom ? Are atomic orbitals parts of the wave function for the whole atom ?

 

[Nugatory]

Google for "Schrödinger equation hydrogen atom"
This thread is closed for real this timre.