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

  1. Jun 23, 2015 #1
    For example, lets 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!)
     
  2. jcsd
  3. Jun 23, 2015 #2

    Nugatory

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    Staff: Mentor

    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).

    This thread is closed.
     
  4. Jun 23, 2015 #3
    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 ?
     
  5. Jun 23, 2015 #3

    Nugatory

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    Staff: Mentor

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