Schrodinger equation the © functions

A key to the application of DFT in handling the interacting electron gas was given by Kohn and Sham [51] who used the variational principle implied by the minimal properties of the energy functional to derive effective singleparticle Schrodinger equations. The functional F[ ] can be split into four parts ... 

Here the form of this eigenfunction follows from the fact that the potential energy of the electron does not depend on the azimuth around the axis, and therefore the coordinate tp can be separated in the Schrodinger equation. The functions and then correspond to the moment 1. Since furthermore we are desding with a state of which the eigenfunction has no node in the middle plane, we have... 

There is a polynomial solution for the radial part of the H atom solution of the Schrodinger equation. The functions are related to previously studied Laguerre polynomials. The total solution for the H atom is the product of the rigid rotor (0, < ) wave functions with the Laguerre radial functions. The eigenvalues for the orbitals are exactly the same as for the... 

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