We introduce a complete set of gauge-invariant variables and a generalized Born-Oppenheimer formulation to search for normalizable zero-energy asymptotic solutions of the Schrodinger equation of SU(2) matrix theory. The asymptotic method gives only ground state candidates, which must be further tested for global stability. Our results include a set of such ground state candidates, including one...

Using the Born-Oppenheimer idea we show that the Wheeler-DeWitt equation in an oscillating regime can also allow a different type of semiclassical quantum gravity that preserves completely the unitary quantum evolution of a matter field, which reduces the same asymptotic limit as the others. We develop a perturbation method to find the quantum corrections of a matter field to the gravity. The s...

Explicitly correlated all-particle Gaussian functions with shifted centers (ECGs) are implemented within the earlier proposed effective variational non-Born-Oppenheimer method for calculating bound states of molecular systems in magnetic field (Adamowicz et al., 2015). The Hamiltonian used in the calculations is obtained by subtracting the operator representing the kinetic energy of the center-...

The unstable manifold of the B = 2 sector of the Skyrme model is constructed numerically using the gradient-flow method. Following paths of steepest descent from the B = 2 hedgehog, we apply a collective coordinate description for the motion on the manifold to extract a Hamiltonian, approximately valid for the quantum description of the low-energy nucleon-nucleon interaction. The resulting pote...

We present a new analytic treatment of two-electron integrals over two-center integrals including correlation (interelectronic distance) explicitly in the wave function. All the integrals needed for the evaluation of the matrix elements of any diatomic two-electron molecule are obtained as analytic recursion expressions. As an application of this method in molecular physics, we calculate the va...

Steven B. Oppenheimer Steven B. Oppenheimer is director of the Center for Cancer and Developmental Biology, California State University, Northridge, CA 91330. He has been named Statewide Trustees Outstanding Professor of the CSU system. Author of about 50 publications in cancer biology, his work includes two texts, Cancer, A Biological and Clinical Introduction and Cancer Prevention Guidebook. ...

This book is a timely read, coinciding as it does with the moving of the renowned Exploratorium from the Palace of Fine Arts at the foot of the Golden Gate Bridge in San Francisco, where it was established in 1969, to its new and larger location at Pier 15 on the Embarcadero. This institution continues to embody the vision of its founder, Frank Oppenheimer, the subject of this highly personal y...

We review mathematical results concerning exponentially small corrections to adiabatic approximations and Born–Oppenheimer approximations.

In this work we give an overview of the methodologies required to compute the rate of proton transfer in hydrogen bonded systems in solution Using ab initio or density functional methods we determine proton potentials of a truncated sys tem as a function of proton donor proton acceptor distance as well as nonbonding parameters By classical molecular dynamics we evaluate a swarm of proton po ten...