Pith Number

pith:HA43IFFW

pith:2026:HA43IFFWA2VO2MEHGKES5M46PD

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Time dependent Schr\"odinger equation for harmonic oscillator in the Aharonov-Bohm magnetic field

Ari Laptev, Jiyu Fan

The propagator kernel for a 2D harmonic oscillator in an Aharonov-Bohm field has a leading term given by a modified Mehler formula.

arxiv:2605.17395 v1 · 2026-05-17 · math.AP · math-ph · math.MP · math.SP

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Record completeness

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Claims

C1strongest claim

For the example considered in this paper we are able to find the main term in the approximation of the kernel that equals a version of the Mehler formula.

C2weakest assumption

The global complex-phase Fourier integral operator machinery developed in the earlier Laptev-Sigal paper applies directly to the Hamiltonian consisting of the 2D harmonic oscillator plus the Aharonov-Bohm vector potential.

C3one line summary

Approximation of the propagator kernel for the 2D harmonic oscillator in Aharonov-Bohm field, with leading term given by a Mehler-type formula, obtained via Fourier integral operators with global complex phases.

References

23 extracted · 23 resolved · 0 Pith anchors

[1] El A ¨ıdi, On a new embedding theorem and the CLR-type inequality for Euclidean and hyperbolic spaces,Bull 2014

[2] Y . Aharonov and D. Bohm, Significance of electromagnetic potentials in the quantum the- ory,Phys. Rev.,15(1959), 485-491 1959

[3] V . M. Babich and V . V . Ulin, Complex space-time ray method and ‘quasiphotons’,(in Russian), Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI )117(1981), 5–11 1981

[4] H. Batelaan and A. Tonomura, The Aharonov–Bohm effects: Variations on a subtle theme, Phys. Today,62(2009), 38-43 2009

[5] R. Beals, B. Gaveau and P.C. Greiner, Hamilton-Jacobi theory and the heat kernel.J. Math. Pures Appl.79, 7 (2000), 633–689 2000

Formal links

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Receipt and verification

First computed	2026-05-20T00:03:56.339906Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3839b414b606aaed308732892eb39e78dc65b1ec27e251d0aac3fd39d146168e

Aliases

arxiv: 2605.17395 · arxiv_version: 2605.17395v1 · doi: 10.48550/arxiv.2605.17395 · pith_short_12: HA43IFFWA2VO · pith_short_16: HA43IFFWA2VO2MEH · pith_short_8: HA43IFFW

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HA43IFFWA2VO2MEHGKES5M46PD \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 3839b414b606aaed308732892eb39e78dc65b1ec27e251d0aac3fd39d146168e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c37d34ee81bd4c061a913c5db47691e99e37c905d4d62c4f8f50271f3fb1843",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-17T11:26:57Z",
    "title_canon_sha256": "648e9a075a9c79af09812b2c7334af60b66a53924beff5ba4204cc40d39216ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17395",
    "kind": "arxiv",
    "version": 1
  }
}