Constructing Wave Function for N-Electron System

[saravanan13]

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>

 

[sokrates]

You construct a single wavefunction:

http://en.wikipedia.org/wiki/Slater_determinant

 

[xepma]

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.

 

[conway]

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?

 

[xepma]

Oh, just that it is the multiparticle version, i.e. the Hamiltonian is:

$$H = \sum_i \frac{1}{2m_i} p_i^2 +V(\lbrace x_i\rbrace)$$

where i runs over all the particles.