相关论文: The Born Oppenheimer wave function near level cros…
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…
We leverage the power of neural quantum states to describe the ground state wave function of solid and liquid atomic hydrogen, including both electronic and protonic degrees of freedom. For static protons, the resulting Born-Oppenheimer…
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…
Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the…
We present a theoretical study of the dissociative tunneling ionization process. Analytic expressions for the nuclear kinetic energy distribution of the ionization rates are derived. A particularly simple expression for the spectrum is…
An analysis of the analytical solution of the Schr\"{o}dinger equation (which is a second order differential equation) for $H_2^+$ shows that the second linear independent solution of this equation is a square integrable function and…
Absolute total cross sections for electron capture between slow, highly charged ions and alkali targets have been recently measured. It is found that these cross sections follow a scaling law with the projectile charge which is different…
A detailed formulation of the relativistic plane-wave Born approximation for inelastic collisions of charged particles with free atoms and positive ions is presented. The wave functions of the target atom or ion are calculated from a…
We investigate the structure of a prototypical two-state conical intersection (BeH$_2$) using a phase space electronic Hamiltonian $\hat{H}_{PS}(\bR,\bP)$ that goes beyond the Born-Oppenheimer framework. By parameterizing the electronic…
The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of…
The electronic Schr\"odinger equation describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wavefunctions, depend on 3N variables, three spatial…
We apply the Born--Oppenheimer approximation to a harmonic diatomic molecule with one electron. We compare the exact and approximate results not only for the internal degrees of freedom but also for the motion of the center of mass. We…
We analyze the quantum states of two atoms in a combined harmonic oscillator and periodic lattice trap in one spatial dimension. In the case of tight-binding and only nearest neighbor tunneling, the equations of motion are conveniently…
Asymptotic levels of the A $^1\Sigma_u^+$ state of the two isotopomers $^{39}{\rm K}_2$ and $^{39}{\rm K}^{41}{\rm K}$ up to the dissociation limit are investigated with a Doppler-free high resolution laser-spectroscopic experiment in a…
The differential cross section of high-energy electroproduction in the electric field of heavy atoms is derived. The result is obtained with the exact account of the atomic field by means of the quasiclassical approximation to the wave…
The Bloch wavefunction leads either to mathematically impossible consequences or suggests that the ground state energy is a function of size and shape when the geometry of large crystals is considered in detail. It is incompatible with the…
Hyperspherical partial wave theory has been applied here in a new way in the calculation of the triple differential cross sections for the ionization of hydrogen atoms by electron impact at low energies for various equal-energy-sharing…
The molecular Schr\"odinger equation is rewritten in terms of non-unitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear)…
The distinction between the charged particle and antiparticle differential cross sections of high-energy bremsstrahlung in the electric field of a heavy atom is investigated. The consideration is based on the quasiclassical approximation to…
In the context of Born-Infeld electrodynamics, the electromagnetic fields interact with each other via their non-linear couplings. A calculation will be performed where an incoming electromagnetic plane wave scatters off a Coulomb Field in…