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It might appear that the diffusion quantum Monte Carlo (DMC) method cannot be applied to excited states because the imaginary time propagation would evolve it towards the ground state. However, the fixed node constraint ensures convergence to the lowest energy state compatible with the nodal surface of the trial wave function. If the nodal surface is exactly that of an eigenstate then DMC gives the exact energy of that state. If the nodal surface is approximately that of an excited state then the DMC energy gives an approximation to the energy of that excited state. There is, however, an important difference from the ground state case, and Foulkes et al. showed how the existence of a variational principle for the energy of an excited state depends on the symmetry of the trial wave function. In practice DMC works quite well for excited states. |
