I. Lineare Fehlerminimisierung Ein Verfahren zur Eigenwertberechnung bei Schrödinger‐Operatoren

A variational principle is derived from the spectral theorem of self‐adjoint operators. The principle allows to calculate simultaneously upper and lower bounds for each point of the spectrum. For Schrödinger operators this method of error minimization is reduced to a series of matrix diagonalizations using an iterative process and is linearized in this way. The convergence of this method and the equivalence with the nonlinear problem of variation are proven.