Semiclassical expansion for exactly solvable differential operators
Abstract
Abstract We investigate the linear differential equation M ( v ( z , η ) ) = η M v ( z , η ) , where η > 0 is a large spectral parameter. The operator M = ∑ k = 1 M ρ k ( z ) d k d z k ( M ⩾ 2 ) has polynomial coefficients where the leading coefficient ρ M ( z ) is a monic complex-valued polynomial of degree M , and deg ρ k ⩽ k for k < M . We prove the Borel summability of its WKB solutions in the Stokes regions. For M = 3 , assuming ρ M has simple zeros, we provide a complete description of the Stokes complex (the union of all Stokes curves). Finally, we demonstrate that for Euler–Cauchy equations, the WKB solutions converge in the standard sense.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Numerical methods for differential equations
Differential Equations and Numerical Methods
Publication details
- Journal / source
- Journal of Physics A Mathematical and Theoretical
- Publisher
- IOP Publishing
- Volume
- 59
- Issue
- 29
- Pages
- 295202–295202
- Publication date
- 6 July 2026
- Language
- EN