We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0 F 3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the ano...

An effective action in Hamiltonian form is derived for a self-gravitating sphere of isotropic homogeneous dust. Starting from the Einstein-Hilbert action for barotropic perfect fluids and making use of the symmetry and equation of state of the matter distribution we obtain a family of reduced actions for two canonical variables, namely the radius of the sphere and its ADM energy, the latter bei...

Factors influencing the rate of reverse intersystem crossing (krISC ) in thermally activated delayed fluorescence (TADF) emitters are critical for improving the efficiency and performance of third-generation heavy-metal-free organic light-emitting diodes (OLEDs). However, present understanding of the TADF mechanism does not extend far beyond a thermal equilibrium between the lowest singlet and ...

For a variety of superconducting qubits, tunable interactions are achieved through mutual inductive coupling to a coupler circuit containing a nonlinear Josephson element. In this paper, we derive the general interaction mediated by such a circuit under the Born-Oppenheimer approximation. This interaction naturally decomposes into a classical part, with origin in the classical circuit equations...

An extension is given for the standard two component model of adiabatic, Born-Oppenheimer (BO) electronic states in a polyatonic molecule, by use of Mathieu functions of arbitrary order. The curl or compatibility conditions for the construction of a diabatic set of states based on a finitedimensional subset of BO states are not satisfied exactly. It is shown, however, that, by successively addi...

A novel treatment of non-adiabatic couplings is proposed. The derivation starts from the long-known, but not well-known, fact that the wave function of the complete system of elctrons and nuclei can be written, without approximation, as a Born-Oppenheimer-type product of a nuclear wavefunction, X(R), and an electronic one, ΦR(r), which depends parametrically on the nuclear configuration R. From...

In 1967, we operated on a patient for cervical cord compression caused by an unusual type of ectopic bone formation in the spinal canal which we tentatively identified as ossification within the posterior longitudinal ligament. Until that time we had believed that calcification of the vertebral ligaments is a phenomenon secondary to spondylosis (Oppenheimer, 1942) and does not cause symptoms by...

We propose an alternative to the usual time–independent Born–Oppenheimer approximation that is specifically designed to describe molecules with non–symmetrical hydrogen bonds. In our approach, the masses of the hydrogen nuclei are scaled differently from those of the heavier nuclei, and we employ a specialized form for the electron energy level surface. As a result, the different vibrational mo...