Analysis of Quartic Potential Problems Using Fredholm Integral Operators with Airy Functions

arXiv:2603.02374 · hep-th, cond-mat.stat-mech, math-ph, math.MP, quant-ph · Submitted 2026-03-02 · Read on arXiv

hep-th, cond-mat.stat-mech, math-ph, math.MP, quant-ph

Submitted: 2026-03-02

Updated: 2026-10-01

Terminology

• Accuracy — 3× in this paper · explained in 1 episode
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Uncommonly accurate energies for the general quartic oscillator
• Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations
• Airy function (exact WKB results for potentials of odd degree)
• Bootstrapping Matrix Quantum Mechanics
• Quantum Mechanical Out-Of-Time-Ordered-Correlators for the Anharmonic (Quartic) Oscillator
• Anharmonic oscillator: a solution
• Comment on: Uncommonly accurate energies for the general quartic oscillator, Int. J. Quantum Chem., e26554 (2020), by P.Okun and K.Burke
• From quartic anharmonic oscillator to double well potential
• An anharmonic alliance: exact WKB meets EPT
• Analytic Model for the Energy Spectrum of the Anharmonic Oscillator
• Convergent perturbative series via finite path integral limits: application to energy at strong coupling of the anharmonic oscillator

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