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

• Quandemonitum
In summary, the wave function ##\psi## describes the quantum state of a particle or system. For a single electron in an atom, the wave function is denoted as ##\psi(q)## and is isolated from the rest of the system. For a hydrogen-like atom with only one electron, the wave function is equivalent to the atomic orbital. In multi-electron atoms where entanglement occurs, the wave function is a non-factorizable function of the coordinates of all particles, and cannot be represented by separate wave functions for each electron. The wave function is a solution to Schrodinger's equation and is associated with the probability of finding a particle in a certain state. The atomic orbitals in a hydrogen atom can be expressed as
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!)

(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 Schrodinger'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).

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 ?

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

## 1. What is the wave function for the whole system/atom?

The wave function for a whole system or atom is a mathematical description of the quantum state of that system. It represents all possible states of the system, including its position, momentum, and other physical properties.

## 2. How is the wave function for a system/atom determined?

The wave function for a system or atom is determined by solving the Schrödinger equation, a fundamental equation in quantum mechanics. This equation takes into account the potential energy of the system and any forces acting on it to determine the wave function.

## 3. What does the wave function represent?

The wave function represents the probability of finding a system or atom in a particular state. The square of the wave function, known as the probability density, gives the probability of finding the system or atom at a specific location or with a specific value for a physical property.

## 4. Can the wave function for a system/atom change over time?

Yes, the wave function for a system or atom can change over time. This is because the Schrödinger equation takes into account the time evolution of the system, meaning that the wave function can change depending on external forces or interactions with other particles.

## 5. How does the wave function relate to the uncertainty principle?

The wave function is related to the uncertainty principle in that it describes the probability of finding a system or atom in a certain state. The uncertainty principle states that there is a fundamental limit to how accurately we can know both the position and momentum of a particle, and the wave function reflects this by showing that the probability of finding a particle at a specific location or with a specific momentum is not definite.

Replies
61
Views
3K
Replies
36
Views
4K
Replies
16
Views
2K
Replies
1
Views
1K
Replies
2
Views
682
Replies
11
Views
1K
Replies
31
Views
4K
Replies
4
Views
893
Replies
5
Views
1K
Replies
9
Views
2K