Excitations as ground state variational parameters

F. Arias de Saavedra, Enrique Buendía

The behaviour of high-order perturbative-variational wavefunctions, with one or more free parameters, is studied. A variational criterion, and a criterion based upon variation of the norm of the perturbative approximation function with order, are used for fixing free parameters. For the quartic anharmonic oscillator, both criteria seem to be equivalent. The obtained energies, not only for the ground state but also for excited states, are in excellent agreement with previous results, although when the authors go to higher excited states they lose precision because of the worsening of the perturbative-variational wavefunctions.

Assa Auerbach

Devin Crowley, Ryan Wilson, Seth T. Rittenhouse +1 more

We investigate the ground state and low-lying excitations of a Bose-Einstein condensate (BEC) of dipolar molecules interacting via short-range contact and long-range dipole­ dipole interactions (ddi). We find the mean field ground state via the variational principle using a separable bosonic wave function as the variational state. This state can be refined to include small excitations in the form of plane waves, and the results of the variational calculation are a set of dispersion relations for the low-lying excitations. We analyze the polarization and stability of the ground state as a function of the strength of the external polarizing electric field, the strength of the ddi, and the strength of the contact interactions. In a certain parameter regime of strong contact interactions that oppose the dipole -dipole interactions, we identify a possible signature of a first -order phase transition: the polarization of the gas discontinuously flips as the electric field is continuously ramped through zero field. By examining the dispersion relations, we find that the ground state in this parameter regime is unstable.

E. Heinz, H. Müther, Harry A. Mavromatis

Ranjan Bhaduri, Yozo Nogami, Chindhu S. Warke

A simple and accurate variational method is formulated and applied to the ground and excited states of the hydrogen atom as well as the hydrogen molecule ion in a homogeneous magnetic field of arbitrary strength. For the ground state, the electronic wave function o is assumed to be a function of a single, appropriately chosen variable R which contains a variational parameter. The functional form of o, and the corresponding energy, are determined by solving a Schr6dinger- like equation, in which the variational parameter appears explicitly in the kinetic and potential energy terms. The variational parameter is optimized by minimizing the lowest eigenvalue of the equation. Excited states may also be obtained by a slight modification of the method, and explicit calculations are carried out for the m1 = - 1 first excited state of hydrogen and the ( )-state of H2 +. Numerical comparisons are made with some recent papers in the literature. Subject headings: atomic processes - magnetic fields - molecular processes - quantum mechanics

H. G. Miller, R. M. Dreizler