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Line 249: In quantum physics, where the spectrum of the [[Hamiltonian (quantum mechanics)\|Hamiltonian]] is the set of discrete energy levels allowed by a quantum mechanical system, the Rayleigh–Ritz method is used to approximate the energy states and wavefunctions of a complicated atomic or nuclear system.<ref name=arfkenweber /> In fact, for any system more complicated than a single hydrogen atom, there is no known exact solution for the spectrum of the Hamiltonian.<ref name=pryce /> In this case, ana [[ansatz\|trial wave function]], <math>\Psi</math>, is tested on the system. This trial function is selected to meet boundary conditions (and any other physical constraints). The exact function is not known; the trial function contains one or more adjustable parameters, which are varied to find a lowest energy configuration. It can be shown that the ground state energy, <math>E_0</math>, satisfies an inequality:

Rayleigh–Ritz method: Difference between revisions