Yousef Saad Department Of Computer Science And Engineering
Yousef Saad Department Of Computer Science And Engineering
Yousef Saad Department Of Computer Science And Engineering
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➤ Hamiltonian H is of the form :<br />
H = − <br />
i<br />
− <br />
i,j<br />
2 ∇ 2 i<br />
2Mi<br />
Zie 2<br />
− <br />
| Ri − rj|<br />
j<br />
+ 1<br />
2<br />
2 ∇ 2 j<br />
2m<br />
<br />
i,j<br />
+ 1<br />
2<br />
<br />
i,j<br />
e2 |ri − rj|<br />
ZiZje 2<br />
| Ri − Rj|<br />
➤ Ψ = Ψ(r1, r2, . . . , rn, R1, R2, . . . , RN) depends on coordinates<br />
of all electrons/nuclei.<br />
➤ Involves sums over all electrons / nuclei and their pairs<br />
➤ Note: ∇ 2 i Ψ is Laplacean of Ψ w.r.t. variable ri. Represents<br />
kinetic energy for i-th particle.<br />
CSE Colloquium 11/09/09 p. 7
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