Variational method (quantum mechanics)

<p>In <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, the variational method is one way of finding <a href="/facts/Approximation/LvYHsXzq">approximations</a> to the lowest energy eigenstate or <a href="/facts/Ground_state/ML7cfCug">ground state</a>, and some excited states. This allows calculating approximate wavefunctions such as <a href="/facts/Molecular_orbital/0dP30jaa">molecular orbitals</a>. The basis for this method is the <a href="/facts/Variational_principle/a5UkKEBj">variational principle</a>.
</p><p>The method consists of choosing a "trial <a href="/facts/Wavefunction/KgM5ykjY">wavefunction</a>" depending on one or more <a href="/facts/Parameter/zFvVFMv9">parameters</a>, and finding the values of these parameters for which the <a href="/facts/Expectation_value_(quantum_mechanics)/szGNS7Dx">expectation value</a> of the energy is the lowest possible. The wavefunction obtained by fixing the parameters to such values is then an approximation to the ground state wavefunction, and the expectation value of the energy in that state is an <a href="/facts/Upper_bound/YJje9oC2">upper bound</a> to the ground state energy.  The <a href="/facts/Hartree%25E2%2580%2593Fock_method/U9mlRWVR">Hartree–Fock method</a>, <a href="/facts/Density_matrix_renormalization_group/06NNgwsH">density matrix renormalization group</a>, and <a href="/facts/Ritz_method/tIn6wYKM">Ritz method</a> apply the variational method.
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Variational method (quantum mechanics) open-in-new

Variational method (quantum mechanics)