Long-time approximation to the evolution of resonant and nonresonant anharmonic oscillators in quantum mechanics

DOI10.1063/1.531799zbMath0872.34060OpenAlexW2060594198MaRDI QIDQ5284270

Albert W. Sáenz

Publication date: 12 October 1997

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531799

zbMATH Keywords

Hilbert spaceinitial value problemselfadjoint operatorsuniform error estimate\(N\)th order approximation

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Applications of operator theory in the physical sciences (47N50) Perturbation theories for operators and differential equations in quantum theory (81Q15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (1)

Lie-series approach to the evolution of resonant and nonresonant anharmonic oscillators in quantum mechanics

Cites Work

• On averaging, reduction, and symmetry in Hamiltonian systems
• On a Hilbert space of analytic functions and an associated integral transform part I
• Nonlinearly coupled oscillators in quantum mechanics: A normal form approach
• Uniqueness and non-uniqueness of normal forms for vector fields
• Time-dependent normal form theory and Schrödinger initial value problems
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS

This page was built for publication: Long-time approximation to the evolution of resonant and nonresonant anharmonic oscillators in quantum mechanics