☆ 4.3 Article

On the quartic anharmonic oscillator and the Pade-approximant averaging method

MODERN PHYSICS LETTERS A (2022)

Related references

Note: Only part of the references are listed.

Article Multidisciplinary Sciences

Methods of Retrieving Large-Variable Exponents

Vyacheslav I. Yukalov et al.

Summary: This article analyzes the methods of determining the characteristic exponents for variables tending to infinity using small-variable asymptotic expansions. Several different methods of summation are compared, and it is found that reliable estimates are obtained when different summation methods are compatible with each other.

SYMMETRY-BASEL (2022)

Add to Collection

Article Engineering, Multidisciplinary

FROM QUARTIC ANHARMONIC OSCILLATOR TO DOUBLE WELL POTENTIAL

Alexander Turbiner et al.

Summary: This study provides highly accurate approximations for the eigenfunctions of the double-well potential by taking a uniformly-accurate approximation for the anharmonic oscillator eigenfunction and forming a function Psi(dw) (u) = Psi(ao)(u)+/- Psi(ao)(u-1).

ACTA POLYTECHNICA (2022)

Add to Collection

Article Chemistry, Physical

Uncommonly accurate energies for the general quartic oscillator

Pavel Okun et al.

Summary: Recent advances in asymptotic analysis of energy levels of potentials have achieved relative errors on the order of 10(-34), solving general quartic and sextic oscillator potentials beyond this level of accuracy. Analytic formulas for expansion in up to three even basis states are provided, confirming the virial theorem for energy components. These benchmark results can be used for extreme tests of approximations in various areas of chemical physics.

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY (2021)

Add to Collection

Editorial Material Chemistry, Physical

Comment on: Uncommonly accurate energies for the general quartic oscillator

Alexander V. Turbiner et al.

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY (2021)

Add to Collection

Article Physics, Multidisciplinary

Anharmonic oscillator: a solution

Alexander Turbiner et al.

Summary: The study shows that in the one-dimensional quantum anharmonic oscillator system, perturbation theory and semiclassical expansion are consistent in terms of energy levels, and the dynamics in x-space and (gx)-space correspond to the same energy spectrum. By deriving the Riccati-Bloch and generalized Bloch equations, it is revealed that perturbation on the logarithmic derivative leads to PT for the RB equation, while the true semiclassical expansion reveals the GB equation, corresponding to a loop expansion in the path integral formalism.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2021)

Add to Collection

Article Multidisciplinary Sciences

Continued Roots, Power Transform and Critical Properties

Simon Gluzman

Summary: The study expands the region of applicability of continued root approximants from convergent to divergent problems through power transformation, successfully tackling challenging issues in calculating critical amplitudes. By optimizing parameters and replacing unknown control parameters, the indeterminate problem is transformed into a determinate and convergent one, leading to accurate solutions for various quantum-mechanical problems.

SYMMETRY-BASEL (2021)

Add to Collection

Article Physics, Nuclear

Radial anharmonic oscillator: Perturbation theory, new semiclassical expansion, approximating eigenfunctions. II. Quartic and sextic anharmonicity cases

J. C. del Valle et al.

INTERNATIONAL JOURNAL OF MODERN PHYSICS A (2020)

Add to Collection

Article Astronomy & Astrophysics

Energy levels of one-dimensional anharmonic oscillator via neural networks

Halil Mutuk

MODERN PHYSICS LETTERS A (2019)

Add to Collection

Article Physics, Nuclear

Radial anharmonic oscillator: Perturbation theory, new semiclassical expansion, approximating eigenfunctions. I. Generalities, cubic anharmonicity case

J. C. del Valle et al.

INTERNATIONAL JOURNAL OF MODERN PHYSICS A (2019)

Add to Collection

Article Physics, Nuclear

Quartic oscillator potential in the γ-rigid regime of the collective geometrical model

R. Budaca

EUROPEAN PHYSICAL JOURNAL A (2014)

Add to Collection

Article Physics, Multidisciplinary

Notes on the Pade Approximation for an Anharmonic Oscillator

Hiroshi Ezawa et al.

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN (2014)

Add to Collection

Article Physics, Fluids & Plasmas

Asymptotic response of observables from divergent weak-coupling expansions: A fractional-calculus-assisted Pade technique

Sharmistha Dhatt et al.

PHYSICAL REVIEW E (2012)

Add to Collection

Article Astronomy & Astrophysics

Anharmonic oscillator energies by the asymptotic iteration method

Hakan Ciftci

MODERN PHYSICS LETTERS A (2008)

Add to Collection

Article Optics

Evaluation of diffraction catastrophes by using Weniger transformation

Riccardo Borghi

OPTICS LETTERS (2007)

Add to Collection

Article Physics, Nuclear

On triplet low-energy parameters of nucleon-nucleon scattering

V. A. Babenko et al.

PHYSICS OF ATOMIC NUCLEI (2006)

Add to Collection

Article Astronomy & Astrophysics

Solution for the eigenenergies of sextic anharmonic oscillator potential V(x) = A6x6 + A4x4 + A2x2

A. J. Sous

MODERN PHYSICS LETTERS A (2006)

Add to Collection

Article Physics, Mathematical

Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators

E. Z. Liverts et al.

JOURNAL OF MATHEMATICAL PHYSICS (2006)

Add to Collection

Article Astronomy & Astrophysics

A perturbative treatment of a generalized PT-symmetric quartic anharmonic oscillator

A Banerjee

MODERN PHYSICS LETTERS A (2005)

Add to Collection

Article Physics, Nuclear

Description of scattering and of a bound state in the two-nucleon system on the basis of the bargmann representation of the S matrix

VA Babenko et al.

PHYSICS OF ATOMIC NUCLEI (2005)

Add to Collection

Review Physics, Multidisciplinary

Divergent perturbation series

IM Suslov

JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS (2005)

Add to Collection

Article Physics, Nuclear

Description of the low-energy doublet neutron-deuteron scattering in terms of parameters characterizing bound and virtual triton states

VA Babenko et al.

PHYSICS OF ATOMIC NUCLEI (2000)

Add to Collection

© Peeref 2019-2024. All rights reserved.