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Chemistry · Glossary

What is Hamiltonian operator?

Definition 1.8 University Chemistry — Year 3 · Chapter 1 — Quantum Mechanics for Chemists: Model Systems

The Hamiltonian operator of a particle of mass mm moving in a potential V(r)V(\mathbf r) is

H^=−ℏ22m∇2+V(r),∇2=∂2∂x2+∂2∂y2+∂2∂z2,\hat H = -\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf r), \qquad \nabla^2 = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2},

and for several particles, the sum of their kinetic terms and of all their potential energies.

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