The quartic oscillator

DOI10.1063/1.531857zbMath0874.39004OpenAlexW2073819607MaRDI QIDQ4338338

Wolfgang Lay

Publication date: 3 November 1997

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

Full work available at URL: https://doi.org/10.1063/1.531857

zbMATH Keywords

Heun's differential equationquantum quartic oscillatorBirkhoff-seteigenvalue-conditionfourth-order linear difference equation of Poincaré-Perron typeJaffé expansion

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Additive difference equations (39A10)

Related Items (7)

Spectral Determinant of the Two‐Photon Quantum Rabi Model ⋮ Manifestation of classical instability in the quantum density of states of a double well potential ⋮ The spectrum of the quartic oscillator ⋮ Open perturbation and the Riccati equation: Algebraic determination of the quartic anharmonic oscillator energies and eigenfunctions ⋮ Bound states and ``resonances in quantum anharmonic oscillators ⋮ The Central Two‐Point Connection Problem in Quantum Mechanics ⋮ Asymptotics of eigenvalue sums when some turning points are complex

Cites Work

• Asymptotic expansions for second-order linear difference equations
• Analytic theory of singular difference equations
• Zur Theorie der Poincaré-Perronschen Differenzengleichungen
• Zur Existenz von Minimallösungen zweifach-unendlicher dreigliedriger linearer Rekursionen vom Poincaré-Perronschen Typ
• Asymptotic Expansions for Second-Order Linear Difference Equations, II
• Exact quantization condition for anharmonic oscillators (in one dimension)

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