Constructing Wave Function for N-Electron System

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Discussion Overview

The discussion revolves around the construction of a wave function for an N-electron system, exploring whether to use one wave function for each electron or a single wave function for the entire system. The scope includes theoretical aspects of quantum mechanics and the implications of particle statistics.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant inquires about the appropriate method for constructing a wave function for an N-electron system, questioning whether to use individual wave functions or a collective one.
  • Another participant asserts that a single wave function should be constructed for the entire system, referencing the concept of Slater determinants.
  • It is noted that the wave function must satisfy the Schrödinger equation for all particle positions, with an emphasis on the requirement for antisymmetry for electrons and symmetry for bosons.
  • A participant seeks clarification on the term "ordinary" Schrödinger equation, prompting a response that it refers to the multiparticle version involving a Hamiltonian that accounts for all particles.

Areas of Agreement / Disagreement

Participants generally agree on the necessity of a single wave function for the N-electron system, but there is some ambiguity regarding the interpretation of the "ordinary" Schrödinger equation and its application to multiple particles.

Contextual Notes

There are unresolved aspects regarding the definitions and implications of the wave function's symmetry properties and the specific form of the Hamiltonian used in the multiparticle context.

saravanan13
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For an N- electron system, how to construct a wave function?
One wave function for each electron or one wave function for the entire system>
 
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A single wavefunction. The same goes for bosons. And this wavefunctions satisfies the "ordinary" schroedinger equation with respect to all the particle positions.

There is, however, an extra condition you impose: statistics. The wavefunction for electrons has to be an anti-symmetric wavefunction -- this is an extra condition you impose.

The same goes for bosons: this must be a symmetric wavefunction.
 
xepma said:
A single wavefunction. The same goes for bosons. And this wavefunctions satisfies the "ordinary" schroedinger equation with respect to all the particle positions.

I wonder what you mean by the "ordinary" schroedinger equation?
 
Oh, just that it is the multiparticle version, i.e. the Hamiltonian is:

[tex]H = \sum_i \frac{1}{2m_i} p_i^2 +V(\lbrace x_i\rbrace)[/tex]

where i runs over all the particles.
 

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