Pith. sign in

REVIEW 1 cited by

Existence and Uniqueness of Exact WKB Solutions for Second-Order Singularly Perturbed Linear ODEs

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2106.10248 v2 pith:O2L2MZ62 submitted 2021-06-18 math.AP math-phmath.CAmath.MP

classification math.APmath-phmath.CAmath.MP
keywords solutionsexactborelcomplexexistenceformallinearodes
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We prove an existence and uniqueness theorem for exact WKB solutions of general singularly perturbed linear second-order ODEs in the complex domain. These include the one-dimensional time-independent complex Schr\"odinger equation. Notably, our results are valid both in the case of generic WKB trajectories as well as closed WKB trajectories. We also explain in what sense exact and formal WKB solutions form a basis. As a corollary of the proof, we establish the Borel summability of formal WKB solutions for a large class of problems, and derive an explicit formula for the Borel transform.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Duck hunting with quantum mechanics

    nlin.PS 2026-08 conditional novelty 6.0 of 10

    For Möbius-type slow-fast systems such as the overdamped Josephson junction, canards exist in parameter windows of width exp(-S_inst/2ω), where S_inst is the β-cycle instanton action.

Pith tools