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Journal of physics. B, Atomic, molecular, and optical physics, ISSN 1361-6455, 2020, Volume 53, Issue 8, p. 85001
We develop a nondirect product discrete variable representation (npDVR) for treating quantum dynamical problems which involve nonseparable angular variables... 
ROTATION | spherical functions | QUANTUM | INVARIANT | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | HYDROGEN-ATOM | discrete variable representation | REACTIVE SCATTERING | Lebedev quandratures on unit sphere | QUADRATURE | OPTICS | nondirect product grid | FORMULAS | Schrodinger equation with nonseparable angular variables
Journal Article
Nature Communications, ISSN 2041-1723, 12/2017, Volume 8, Issue 1, pp. 1306 - 12
Journal Article
Mathematical Physics, Analysis and Geometry, ISSN 1385-0172, 4/2003, Volume 6, Issue 4, pp. 301 - 348
The method of separation of variables applied to the natural Hamilton–Jacobi equation $${\frac{1}{2}}$$ ∑(∂u/∂q i )2+V(q)=E consists of finding new curvilinear coordinates x... 
Geometry | integrability | Hamilton–Jacobi equation | Analysis | Mathematical and Computational Physics | Group Theory and Generalizations | Applications of Mathematics | separation of variables | Physics | Schrödinger equation | Separation of variables | Hamilton-Jacobi equation | Integrability | MATHEMATICS, APPLIED | Schrodinger equation | MOTION | TRAP | POTENTIALS | PHYSICS, MATHEMATICAL
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 12/2007, Volume 48, Issue 12, pp. 122701 - 122701-19
... quadratic Hamiltonian that can be described by different methods, namely, the time-dependent Schrödinger equation, the time propagator or Feynman kernel, and the Wigner function is connected via a dynamical invariant, the so-called Ermakov invariant... 
DERIVATION | FRICTION | LANGEVIN EQUATION | NONLINEAR SCHRODINGER-EQUATIONS | MOTION | EXAMPLE | FIELD EQUATION | PHYSICS, MATHEMATICAL | EVOLUTION | SCHROEDINGER EQUATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | HAMILTONIANS | FUNCTIONS | QUANTUM MECHANICS | TIME DEPENDENCE | PROPAGATOR
Journal Article
Journal of Mathematical Chemistry, ISSN 0259-9791, 6/2012, Volume 50, Issue 6, pp. 1420 - 1436
We consider the problem of defining the Schrödinger equation for a hydrogen atom on $${\mathbb{R}^3 \times \mathcal{M}}$$ where $${\mathcal{M... 
Theoretical and Computational Chemistry | Chemistry | Compact extra dimensions | Physical Chemistry | Eigen value problem | Hydrogen atom | Math. Applications in Chemistry | Schrödinger equation | Non-separable potential
Journal Article
Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, 09/2002, Volume 35, Issue 18, pp. R147 - R193
Atomic stabilization is a highlight of superintense laser-atom physics. A wealth of information has been gathered on it; established physical concepts have... 
FREQUENCY FLOQUET-THEORY | DYNAMIC STABILIZATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | MULTIPHOTON IONIZATION | SHORT-PULSE | HYDROGEN-ATOM | RYDBERG ATOMS | OPTICS | RANGE MODEL ATOM | ADIABATIC STABILIZATION | DEPENDENT SCHRODINGER-EQUATION | ELECTRON LOCALIZATION
Journal Article
Chinese Physics Letters, ISSN 0256-307X, 06/2008, Volume 25, Issue 6, pp. 2008 - 2011
A robust time-dependent approach to the high-resolution photoabsorption spectrum of Rydberg atoms in magnetic fields is presented. Traditionally we have to... 
TRANSITION | HYDROGEN-ATOM | PHYSICS, MULTIDISCIPLINARY | REGULARITY | SCHRODINGER-EQUATION | B-SPLINE
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 10/1995, Volume 36, Issue 10, pp. 5355 - 5391
...Quantized Neumann problem, separable potentials on S” and the Lam6 equation David Gurarie Case Western Reserve University Cleveland, Ohio 44106 (Received 20... 
ASYMPTOTICS | PHYSICS, MATHEMATICAL | INVERSE SPECTRAL PROBLEM | SPHERE | SCHRODINGER-OPERATORS
Journal Article
Journal of Physics A: Mathematical and General, ISSN 0305-4470, 08/1997, Volume 30, Issue 16, pp. 5825 - 5833
We present a method for calculating the energies of bound and quasibound states of quantum-mechanical problems expressed in terms of coupled-channel equations... 
EIGENVALUES | STATES | MAGNETIC-FIELDS | K UR PHYSICS, MATHEMATICAL | SCHRODINGER-EQUATION | ENERGY-LEVELS | ATOMS | K UI PHYSICS | PHYSICS | PHYSICS, MATHEMATICAL
Journal Article
International Journal of Theoretical Physics, ISSN 0020-7748, 6/1998, Volume 37, Issue 6, pp. 1793 - 1856
Journal Article
Journal of Physics A: Mathematical and General, ISSN 0305-4470, 06/1996, Volume 29, Issue 12, pp. 3167 - 3177
We discuss a quantization condition for bound and quasibound states of separable quantum-mechanical systems. Results for simple non-trivial models suggest that... 
SPECTRUM | PHYSICS, MATHEMATICAL | SCHRODINGER-EQUATION | ENERGY EIGENVALUES
Journal Article
Journal of physics. A, Mathematical and general, ISSN 1361-6447, 1998, Volume 31, Issue 2, pp. 779 - 788
The vibrational levels of diatomic molecules via Morse potentials are studied by means of the system confined in a spherical box of radius l, II is shown that... 
ENERGY-SPECTRUM | MULTIMINIMA | EIGENVALUES | PHYSICS, MULTIDISCIPLINARY | BOUNDS | SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | OSCILLATOR
Journal Article
Journal of Mathematical Chemistry, ISSN 0259-9791, 12/1997, Volume 22, Issue 1, pp. 11 - 23
Energy eigenvalues of double‐well potentials for two‐dimensional systems are calculated by the approach of expanding the potential functions such as... 
Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Math. Applications in Chemistry | ANHARMONIC-OSCILLATORS | EIGENVALUES | MATHEMATICS, APPLIED | HILL DETERMINANT APPROACH | SCHRODINGER-EQUATION | VARIATIONAL CALCULATIONS | CHEMISTRY, MULTIDISCIPLINARY
Journal Article
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