The variational principle is revisited in the context of finding the upper and lower bounds to the ground state energy. It is shown how the variational principle can be employed to find the lower bound by partitioning the Hamiltonian into several parts. We demonstrate how the variational principle can be used to find the exact ground states in some special cases. We consider the harmonic oscillator and the Ising Hamiltonian on a bipartite lattice which are familiar yet instructive examples for students.
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2009
American Association of Physics Teachers
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