To use the variation principle for a given problem you do no

To use the variation principle for a given problem, you do not need to know the stationary state wave functions in order to estimate the ground state energy for a particle in the system. What minimum information do you need to know?

Solution

The method consists in 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 and the Ritz method both apply the variational method.