Excited States in Variational Many-Body Approaches

A method is implemented wherein numerical approximations to the ground and first few excited states of a quantum mechanical N -body 1D harmonic oscillator are found through variational methods, representing the states as a linear combination of normalized pseudo-states which are themselves linear combinations of non-orthogonal Slater determinants. These states are then used as a low energy basis for configuration interaction. An expression is derived for an analytical matrix derivative of the energy functional, in order to improve the speed of the variation. The speed and accuracy using the analytical derivative is compared to that of the numerical derivative, and a number of different gradient descent methods are tried and compared