In materials simulations the external potential Vext is usually the
interaction of the electrons with the nuclei. Thus:
( )
1
N
ext
Z
V
a
a
a = a
=
−
r
r R
The separation of electron and nuclear degrees of freedom is valid
under the Born-Oppenheimer approximation. Relativistic effects are neglected
neglected.
The external potential and the number of electrons therefore
completely determine the Hamiltonian H.
We assume for simplicity a nondegenerate ground state. Then the
wave function must be anti-symmetric under exchange
of its arguments (Pauli-principle) and we assume
is normalized.-----------
氫原子核對電子Born-Oppenheimer approximation Relativistic effects
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