The Method of Lagrange Multipliers — Finding the Lowest Point Under a Constraint

“While satisfying a condition, minimize (or maximize) something.” Physics is full of problems of this form. Here we take the expectation value of the energy of a molecule AB as an example and look at what is going on on the plane of the coefficients c_A, c_B. From there the secular equation emerges, and we arrive at bonding and antibonding orbitals.

Mochizuki Research Group, Tokyo University of Science | Based on Lecture 11, “The Secular Equation and the Covalent Bond,” of the course “Computational Materials Science.” The derivation of the equations is on the explanation page (in Japanese).