A01=Alexander Turbiner
A01=Juan Carlos Del Valle Rosales
Anharmonic Oscillator
Anharmonic Potentials
Asymptotic Series
Author_Alexander Turbiner
Author_Juan Carlos Del Valle Rosales
Borel Summation
Category=PHU
Cubic Anharmonic Oscillator
Divergent Series
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Generalized Bloch Equation
Lagrange Mesh Method
Locally Accurate Approximations
Logarithmic Perturbation Theory
Non-solvable Systems
Nonlinear Oscillators
Nonlinearization Procedure
PadAfA(C)-Borel Summation
Pade-Borel Summation
Perturbation Theory
Polynomial Potentials
Quantum Mechanics
Quantum Oscillator
Quartic Anharmonic Oscillator
Radial Anharmonic Oscillators
Riccati-Bloch Equation
Semiclassical expansions
Sextic Anharmonic Oscillator
Variational Method
WKB approximation
Product details
- ISBN 9789811270451
- Publication Date: 24 Mar 2023
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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Quartic anharmonic oscillator with potential V(x)= x² + g²x⁴ was the first non-exactly-solvable problem tackled by the newly-written Schrödinger equation in 1926. Since that time thousands of articles have been published on the subject, mostly about the domain of small g² (weak coupling regime), although physics corresponds to g² ~ 1, and they were mostly about energies.This book is focused on studying eigenfunctions as a primary object for any g². Perturbation theory in g² for the logarithm of the wavefunction is matched to the true semiclassical expansion in powers of ℏ: it leads to locally-highly-accurate, uniform approximation valid for any g²∈[0,∞) for eigenfunctions and even more accurate results for eigenvalues. This method of matching can be easily extended to the general anharmonic oscillator as well as to the radial oscillators. Quartic, sextic and cubic (for radial case) oscillators are considered in detail as well as quartic double-well potential.
