Variational method for excited states from supersymmetric techniques - Borges, G. R P [UNESP]; Dutra, Alvaro de Souza [UNESP]; Drigo Filho, Elso [UNESP]; Ruggiero, José Roberto [UNESP] (Canadian Science Publishing, 2003)
We suggest a method for constructing trial eigenfunctions for excited states to be used in the variational method. This method is a generalization of the one that uses a superpotential to obtain the trial functions for the ground state. The construction of an effective hierarchy of Hamiltonians is used to determine excited variational energies. The first four eigenvalues for a quartic double-well potential are calculated for several values of the potential parameter. The results are in very good agreement with the eigenvalues obtained by numerical integration.
Keywords: Algebra; Eigenvalues and eigenfunctions; Excitons; Ground state; Hamiltonians; Perturbation techniques; Riccati equations; Supersymmetric formalism; Variational method; Quantum theory