Exact 2-component energies/results

As one can see, for each set of parameters Z, k, L and d, one can select a in such a way that Eqs. (21) and (22) are fulfilled. Then, the resulting expectation values correspond to the variational minima and are equal to the appropriate exact eigenvalues of either Dirac or Schrodinger (or rather Levy-Leblond) Hamiltonian. However the corresponding functions do not fulfil the pertinent eigenvalue equations they are not eigenfunctions of these Hamiltonians. This example demonstrates that the value of the variational energy cannot be taken as a measure of the quality of the wavefunction, unless the appropriate relation between the components of the wavefunction is fulfilled [2]. 

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