arXiv subjects
Publications and source records attributed to David J Fernandez C.
The hyperconfluent third-order supersymmetric quantum mechanics, in which all the factorization energies tend to a common value, is analyzed. It will be shown that the final potential as well can be achieved by applying consecutively a confluent second-order and a first-order SUSY transformations, both with the same factorization energy. The technique will be applied to the free particle and the Coulomb potential.
The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows to identify directly the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and they are going to be compared with those attained through the displacement operator method. The corresponding wave function will be found, and a general procedure for obtaining several expected values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.
The general solution of the stationary Schrodinger equation for the associated Lame potentials with an arbitrary real energy is found. The supersymmetric partners are generated by employing seeds solutions for factorization energies inside the gaps.
By using a matrix technique, which allows to identify directly the ladder operators, the Penning trap coherent states are derived as eigenstates of the appropriate annihilation operators. These states are compared with the ones obtained through the displacement operator. The associated wave functions and mean values for some relevant operators in these states are also evaluated. It turns out that the Penning trap coherent states minimize the Heisenberg uncertainty relation.
The first and second-order supersymmetry transformations are used to generate Hamiltonians with known spectra departing from the trigonometric Poschl-Teller potentials. The several possibilities of manipulating the initial spectrum are fully explored, and it is shown how to modify one or two levels, or even to leave the spectrum unaffected. The behavior of the new potentials at the boundaries of the domain is studied.
The Aharonov-Anandan and Berry phases are determined for the cyclic motions of a non-relativistic charged spinless particle evolving in the superposition of the fields produced by a Penning trap and a rotating magnetic field. Discussion about the selection of the parameter's space and the relationship between the Berry phase and the symmetry of the binding potential is given.
We obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The formalism of supersymmetric quantum mechanics is used to generate new exactly solvable potentials.
We review the higher-order supersymmetric quantum mechanics (H-SUSY QM), which involves differential intertwining operators of order greater than one. The iterations of first-order SUSY transformations are used to derive in a simple way the higher-order case. The second order technique is addressed directly, and through this approach unexpected possibilities for designing spectra are uncovered. The formalism is applied to the harmonic oscillator: the corresponding H-SUSY partner Hamiltonians are ruled by polynomial Heisenberg algebras which allow a straight construction of the coherent states.