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Variational method (quantum mechanics)

In quantum mechanics, the variational method is one way of finding approximations to the lowest energy eigenstate or ground state, and some excited states. This allows calculating approximate wavefunctions such as molecular orbitals.[1] The basis for this method is the variational principle.[2][3]

The method consists of choosing a "trial wavefunction" depending on one or more parameters, and finding the values of these parameters for which the expectation value 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 upper bound to the ground state energy. The Hartree–Fock method, density matrix renormalization group, and Ritz method apply the variational method.

  1. ^ Sommerfeld, Thomas (2011-11-01). "Lorentz Trial Function for the Hydrogen Atom: A Simple, Elegant Exercise". Journal of Chemical Education. 88 (11): 1521–1524. Bibcode:2011JChEd..88.1521S. doi:10.1021/ed200040e. ISSN 0021-9584.
  2. ^ Griffiths, D. J. (1995). Introduction to Quantum Mechanics. Upper Saddle River, New Jersey: Prentice Hall. ISBN 978-0-13-124405-4.
  3. ^ Sakurai, J. J. (1994). Tuan, San Fu (ed.). Modern Quantum Mechanics (Revised ed.). Addison–Wesley. ISBN 978-0-201-53929-5.

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