Borel summability: Application to the anharmonic oscillator

S. Graffi, V. Grecchi, Barry Simon

Type: Article

Publication Date: 1970-08-01

Citations: 291

DOI: https://doi.org/10.1016/0370-2693(70)90564-2

View Publication

Download PDF

Locations

Physics Letters B - View
INFM-OAR (INFN Catania) - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Borel Summability: Application to the Anharmonic Oscillator	1990	S. GRAFFI V. GRECCHI B. SIMON
+	Summation methods for the perturbation series of the generalized anharmonic oscillator	1971	S. Graffi V. Grecchi G. Turchetti
+	Borel summability and indeterminacy of the Stieltjes moment problem: Application to the anharmonic oscillators	1978	S. Graffi V. Grecchi
+	Large orders and summability of eigenvalue perturbation theory: A mathematical overview	1982	Barry Simon
+ PDF Chat	Solving the anharmonic oscillator: tuning the boundary condition	2007	David Léonard Paul Mansfield
+ PDF Chat	Borel Summability of the Ground-State Energy in Spatially Cutoff<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>	1970	Barry Simon
+	Padé summability of the cubic oscillator	2009	V. Grecchi Marco Maioli André Martínez
+ PDF Chat	Topological expansion and exponential asymptotics in 1D quantum mechanics	2000	Stefan Giller
+ PDF Chat	Distributional Borel summability of odd anharmonic oscillators	2000	Emanuela Caliceti
+	Summation of divergent series by order dependent mappings: Application to the anharmonic oscillator and critical exponents in field theory	1979	R. Seznec Jean Zinn‐Justin
+	Borel Resummation Method with Conformal Mapping and the Ground State Energy of the Quartic Anharmonic Oscillator	2024	Wajdi A Gaddah Ibrahim S. Jwan
+ PDF Chat	On the quantum anharmonic oscillator and Padé approximations	2021	В. А. Бабенко N. M. Petrov
+	A Modified Borel Summation Technique	2007	David Léonard Paul Mansfield
+	Quantum Field Theory as a Problem of Resummation (Short guide to using summability methods)	1992	Alexander Moroz
+	Approximation for periodic functions via statistical A-summability	2017	Sevda Karakuş Kami̇l Demi̇rci̇
+	Quantum Field Theory as a Problem of Resummation (Short guide to using summability methods)	1992	Alexander Moroz
+	The Borel Summability of Fourier Series	1926	M. H. Stone
+	Borel summability of the conjugate series of a derived Fourier series	1955	S. D. Sinvhal
+	Summation of divergent series: Order-dependent mapping	2010	Jean Zinn‐Justin
+	Summation of divergent series: Order-dependent mapping	2010	Jean Zinn‐Justin

Works That Cite This (155)

Action	Title	Year	Authors
+ PDF Chat	On functions uniquely determined by their asymptotic expansion	2006	D. W. H. Gillam V. P. Gurariĭ
+	Quantum singular complete integrability	2016	Thierry Paul Laurent Stolovitch
+ PDF Chat	Relativistic solutions of generalized-Dunkl harmonic and anharmonic oscillators	2022	S. Hassanabadi Jan Křı́ž B. C. Lütfüoğlu H. Hassanabadi
+	An improvement of Watson’s theorem on Borel summability	1980	Alan D. Sokal
+ PDF Chat	From useful algorithms for slowly convergent series to physical predictions based on divergent perturbative expansions	2007	Emanuela Caliceti Michael Meyer‐Hermann Paolo Ribeca A. Surzhykov Ulrich D. Jentschura
+ PDF Chat	Optimized Self-Similar Borel Summation	2023	S. Gluzman V. I. Yukalov
+	XI. The Borel transform and the renormalization group	1979	Giorgio Parisi
+	Some properties of Borel summable functions	1981	G. Auberson G. Mennessier
+ PDF Chat	Modified Padé–Borel Summation	2023	S. Gluzman
+ PDF Chat	Fast summation of divergent series and resurgent transseries from Meijer- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>G</mml:mi></mml:math> approximants	2018	Héctor Mera Thomas Garm Pedersen Branislav K. Nikolić

Works Cited by This (2)

Action	Title	Year	Authors
+	Summability Methods in Perturbation Theory	1970	Michael Reeken
+ PDF Chat	Pade approximants and the anharmonic oscillator	1969	J. J. Loeffel A. Martin Barry Simon A. S. Wightman