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

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

The Journal of Chemical Physics, ISSN 0021-9606, 1993, Volume 99, Issue 5, pp. 3411 - 3419

It is shown that the cumulative reaction probability for a chemical reaction can be expressed (absolutely rigorously) as N(E) = SIGMA(k)p(k)(E), where {p(k)}...

THERMAL RATE CONSTANTS | QUANTUM | DISCRETE VARIABLE REPRESENTATION | NONSEPARABLE SYSTEMS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | MECHANICAL RATE CONSTANTS | FLUX AUTOCORRELATION FUNCTION | DEPENDENT SCHRODINGER-EQUATION | ABSORBING BOUNDARY-CONDITIONS | SCATTERING | TRANSITION-STATE THEORY | 400201 - Chemical & Physicochemical Properties | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CALCULATION METHODS | INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY | HERMITIAN MATRIX | NONMETALS | COLLISIONS | ATOM COLLISIONS | EIGENVALUES | HYDROGEN | ANGULAR MOMENTUM | ELEMENTS | PROBABILITY | 661100 - Classical & Quantum Mechanics- (1992-) | MATRICES | CHEMICAL REACTIONS | ATOM-MOLECULE COLLISIONS | MOLECULE COLLISIONS | ITERATIVE METHODS

THERMAL RATE CONSTANTS | QUANTUM | DISCRETE VARIABLE REPRESENTATION | NONSEPARABLE SYSTEMS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | MECHANICAL RATE CONSTANTS | FLUX AUTOCORRELATION FUNCTION | DEPENDENT SCHRODINGER-EQUATION | ABSORBING BOUNDARY-CONDITIONS | SCATTERING | TRANSITION-STATE THEORY | 400201 - Chemical & Physicochemical Properties | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CALCULATION METHODS | INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY | HERMITIAN MATRIX | NONMETALS | COLLISIONS | ATOM COLLISIONS | EIGENVALUES | HYDROGEN | ANGULAR MOMENTUM | ELEMENTS | PROBABILITY | 661100 - Classical & Quantum Mechanics- (1992-) | MATRICES | CHEMICAL REACTIONS | ATOM-MOLECULE COLLISIONS | MOLECULE COLLISIONS | ITERATIVE METHODS

Journal Article

Nature Communications, ISSN 2041-1723, 12/2017, Volume 8, Issue 1, pp. 1306 - 12

.... But two axioms distinguish quantum mechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global...

DERIVATION | HIDDEN-VARIABLES | EINSTEIN | INFORMATION | MULTIDISCIPLINARY SCIENCES | SCHRODINGER-EQUATION | VIEW | Statistical analysis | Epistemology | Conservation | Entanglement | Statistics | Quantum physics | Axioms | Classical mechanics | Energy conservation | Quantum mechanics | Randomness | Random variables | Statistical mechanics | Quantum theory | Physics - Quantum Physics

DERIVATION | HIDDEN-VARIABLES | EINSTEIN | INFORMATION | MULTIDISCIPLINARY SCIENCES | SCHRODINGER-EQUATION | VIEW | Statistical analysis | Epistemology | Conservation | Entanglement | Statistics | Quantum physics | Axioms | Classical mechanics | Energy conservation | Quantum mechanics | Randomness | Random variables | Statistical mechanics | Quantum theory | Physics - Quantum Physics

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

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

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

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

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

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

ASYMPTOTICS | PHYSICS, MATHEMATICAL | INVERSE SPECTRAL PROBLEM | SPHERE | SCHRODINGER-OPERATORS

Journal Article

Quantum Information Processing, ISSN 1570-0755, 9/2015, Volume 14, Issue 9, pp. 3279 - 3302

... ) perturbations and then solving the Schrödinger equation to obtain the evolution operator at time T up to $$O({e}^2)$$ O ( e 2...

Quantum Computing | Perturbation theory | Data Structures, Cryptology and Information Theory | Lagrange multiplier | Mathematical Physics | Dyson series | Quantum Information Technology, Spintronics | Quantum Physics | Quantum gate | Physics | Schrödinger equation | 3-D quantum harmonic oscillators | STATES | UNIVERSAL | PHYSICS, MULTIDISCIPLINARY | COHERENT | PHYSICS, MATHEMATICAL | ALGEBRAS | Schrodinger equation | COMPUTATION | Signal processing | Electromagnetic fields | Digital signal processors | Analysis

Quantum Computing | Perturbation theory | Data Structures, Cryptology and Information Theory | Lagrange multiplier | Mathematical Physics | Dyson series | Quantum Information Technology, Spintronics | Quantum Physics | Quantum gate | Physics | Schrödinger equation | 3-D quantum harmonic oscillators | STATES | UNIVERSAL | PHYSICS, MULTIDISCIPLINARY | COHERENT | PHYSICS, MATHEMATICAL | ALGEBRAS | Schrodinger equation | COMPUTATION | Signal processing | Electromagnetic fields | Digital signal processors | Analysis

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

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

In the present work, we survey various methodsused for the construction of exact invariants fordynamical systems involving an explicit time dependence.More...

Quantum Physics | Physics, general | Mathematical and Computational Physics | Physics | Elementary Particles, Quantum Field Theory | ANHARMONIC-OSCILLATORS | HARMONIC-OSCILLATOR | NUMERICAL-SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | GENERALIZED ERMAKOV SYSTEMS | HAMILTONIAN-SYSTEMS | DIFFERENTIAL-EQUATION | SCHRODINGER-EQUATION | FEYNMAN PROPAGATOR | QUANTUM-MECHANICS | 2 DIMENSIONS

Quantum Physics | Physics, general | Mathematical and Computational Physics | Physics | Elementary Particles, Quantum Field Theory | ANHARMONIC-OSCILLATORS | HARMONIC-OSCILLATOR | NUMERICAL-SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | GENERALIZED ERMAKOV SYSTEMS | HAMILTONIAN-SYSTEMS | DIFFERENTIAL-EQUATION | SCHRODINGER-EQUATION | FEYNMAN PROPAGATOR | QUANTUM-MECHANICS | 2 DIMENSIONS

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

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

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

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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