Electron density in terms of squares of wavefunctions

[Physicslad78]

Dear all,

I have a quantum system made up of two layers. An electric field is applied with two voltages applied at both layers. I want to calculate the electronic densities that reside at the two laters in terms of the wavefunctions obtained from solving the HamiltoniaN..Anyone knows of an expression relating the electronic densities with the squares of the wavefunctions or anywhere I can find this expression?

Thanks

Elie

 

[K^2]

Square of the wave function is the probability density. But if you have multiple particles, your wave function will be quite complex.

 

[Physicslad78]

Hello,

In fact I am working with bilayer graphene under the effect of an external voltage. bilayer graphene has 4 bands 2 valence and 2 conduction ones. when u apply a field some excess charge will acuumulate at the 2 layers; I read that this excess charge density is proportional to the square of the wavefunction but can't get hold of the exact expression.


Thank you