Related papers: Analytic description of inversion vibrational mode…
The one-dimensional Schr\"odinger equation with symmetric trigonometric double-well potential (DWP) is exactly solved via angular oblate spheroidal function. The results of stringent analytic calculation for the ground state splitting of…
The exact solution of the one-dimensional Schr\"odinger equation with symmetric trigonometric double-well potential (DWP) is obtained via angular oblate spheroidal function. The results of stringent analytic calculation for the ground state…
The reduced mass of the effective quantum particle for the inversion mode $\nu_2$ of phosphine molecule ${\rm{PH_3}}$ is known to be a position dependent one. In the present article the inversion spectrum of ${\rm{PH_3}}$ is considered with…
We introduce a general approach for the simulation of quantum vibrational states of (symmetric and asymmetric) double-well potentials in molecules and materials for thermodynamic and spectroscopic applications. The method involves solving…
Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also…
We solve the stationary Schr\"odinger equation for a particle confined to a 3D spherical wedge -- the region $\{(r,\theta,\phi): 0 \leq r \leq R,\, 0 \leq \theta \leq \pi,\, 0 \leq \phi \leq \Phi\}$ with Dirichlet BCs on all surfaces. This…
A second-order supersymmetric transformation is presented, for the two-channel Schr\"odinger equation with equal thresholds. It adds a Breit-Wigner term to the mixing parameter, without modifying the eigenphase shifts, and modifies the…
We analyze one particle, two-center quantum problems which admit separation of variables in prolate spheroidal coordinates, a natural restriction satisfied by the H$_2^+$ molecular ion. The symmetry operator is constructed explicitly. We…
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…
We demonstrate that the Schr\"odinger equation for two electrons on a ring, which is the usual paradigm to model quantum rings, is solvable in closed form for particular values of the radius. We show that both polynomial and irrational…
We relax the usual diagonal constraint on the matrix representation of the eigenvalue wave equation by allowing it to be tridiagonal. This results in a larger solution space that incorporates an exact analytic solution for the non-central…
Spin-weighted spheroidal harmonics play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering. We present a novel and compact derivation of the asymptotic…
Nelson's stochastic mechanics formulates quantum dynamics as a real-time conservative diffusion process in which a particle undergoes Brownian-like motion with a fluctuation amplitude fixed by Planck's constant. While being mathematically…
We outline a remarkably efficient method for generating solutions to quantum anharmonic oscillators with an x^{2M} potential. We solve the Schroedinger equation in terms of a free parameter which is then tuned to give the correct boundary…
We present a theoretical study of the mixed-field-orientation of asymmetric top molecules in tilted static electric field and non-resonant linearly polarized laser pulse by solving the time-dependent Schr\"odinger equation. Within this…
We found that the two-dimensional Schr\"odinger equation for 3 electrons in an homogeneous magnetic field (perpendicular to the plane) and a parabolic scalar confinement potential (frequency $\omega_0$) has exact analytical solutions in the…
We study the symmetric periodic Anderson model of the conduction electrons hybridized with the localized correlated electrons on square lattice. Using the canonical representation of electrons by Kumar, we do a self-consistent theory of its…
We present a direct ab initio solution of the Schrodinger equation for neutral helium and helium-like atoms that reproduces the energy of the singlet S state 1S0. By redefining the two-electron wavefunction with tools from complex analysis…
The Schrodinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate ro-vibratinal energy…
A theoretical scheme for the analysis of experimental data on IR spectroscopy for a quantum particle in a double well potential (DWP) is suggested. The analysis is based on the trigonometric DWP for which the exact analytic solution of the…