Lower bounds to ground state eigenvalues of the Schroedinger equation via optimized inner projection: application to quartic and sextic anharmonic oscillators

Inner projection combined with bracketing techniques represents a very powerful method of calculating lower bounds to eigenvalues of the Schroedinger equation. The Hamiltonian is expressed as a sum of an unperturbed operator (whose eigenvalue equation is soluble) and a perturbed operator that should be positive definite. For small values of the coupling constant, the conventional splitting of the Hamiltonian is adequate. For strong coupling, however, it is advantageous to partition the Hamiltonian in an optimized fashion, accomplished by an appropriate scaling of the space coordinates and momenta. This optimized inner projection (OIP) method yields remarkably good results for all values of the coupling constant, even for manifolds of minimal dimensionality