The variational principle is a method in quantum mechanics and physics that provides an approximate solution to a problem by minimizing the energy of a trial wave function. It states that for a given Hamiltonian, the expectation value of the energy calculated with any normalized trial wave function will always be greater than or equal to the true ground state energy, making it a powerful tool for finding the lowest energy states in many-body systems. This principle plays a significant role in the Hartree-Fock method and self-consistent field approaches by helping to optimize wave functions for multi-electron systems.
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