Paper Citation Record · LEDGER

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space

As of 22 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 1 inbound Pith citation observation for arXiv:2501.14831.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2501.14831 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T16:17:12.957392Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-09T04:37:34.897162Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-09T04:37:35.668818Z

Reference resolution

32 of 32 outbound references displayed

verified exact5
verified fuzzy10
unresolved14
parse uncertain0
malformed identifier2
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c21a261f-c093-48ba-ae5b-039477d5ce68 · outbound

This paper cites [11]) uses the orthogo- nality property as R ∞ 0 zae−zLa b (z)La c (z)dz = Γ(a+b+1) [Γ(b+1)]3 δbc, but this will not affect in our calculation, we see.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space [11]) uses the orthogo- nality property as R ∞ 0 zae−zLa b (z)La c (z)dz = Γ(a+b+1) [Γ(b+1)]3 δbc, but this will not affect in our calculation, we see

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:13.701080Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6fb6d126-49c7-409e-b08f-b6da65c1edf0 · outbound

This paper cites an unresolved cited work.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:17:13.684849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 51d63f41-99af-4248-9069-37f76cff174c · outbound

This paper cites an unresolved cited work.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:17:13.666118Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8bef51f6-a7df-477e-92c7-8d95f4df0169 · outbound

This paper cites They are tabulated in Table III.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space They are tabulated in Table III

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:13.647876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f907f8d7-86fa-44fa-bb0e-6437f93576ad · outbound

This paper cites an unresolved cited work.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:17:13.624567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 758d0f36-80c1-4785-a0b7-f402805312c0 · outbound

This paper cites the ratio of uncertainty and expectation of radial FIG.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space the ratio of uncertainty and expectation of radial FIG

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:13.603713Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5ef70939-ef99-4d6c-bec6-c5b1bb9e434b · outbound

This paper cites Now it is known that the radial prob- ability current is directly proportional to average radial momentum.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Now it is known that the radial prob- ability current is directly proportional to average radial momentum

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:13.585528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation aeca6dee-59f9-4b5a-b8f1-c9c041ccf6e8 · outbound

This paper cites If ℓ = 0, then ∆ˆpr = Zℏ na0 and for ground state wave function (n = 1, ℓ= 0), it becomes ∆ˆpr = Zℏ a0.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space If ℓ = 0, then ∆ˆpr = Zℏ na0 and for ground state wave function (n = 1, ℓ= 0), it becomes ∆ˆpr = Zℏ a0

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:13.567209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 12b6cc4c-a152-45a7-8402-5413da34f561 · outbound

This paper cites They are tabulated in Table IV.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space They are tabulated in Table IV

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:13.548815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 22503250-119d-4623-a808-0e98c6f63f2f · outbound

This paper cites Uncertainties in radial position, momentum and their product FIG.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Uncertainties in radial position, momentum and their product FIG

Reference 10

Resolution: malformed identifier; raw_fallback, observed 2026-08-10T16:17:13.530163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4a0df797-bc08-4801-b7fc-82f5ea301ee9 · outbound

This paper cites https://doi.org/10.1142/S0217979222500722.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space https://doi.org/10.1142/S0217979222500722

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-10T16:17:12.856127Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f5705a69-791f-4d78-a284-824c9c85ab21 · outbound

This paper cites https://doi.org/ 10.1119/1.3534840.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space https://doi.org/ 10.1119/1.3534840

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-10T16:17:12.861297Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 693279f2-fe72-4205-aa02-32e4c87e6112 · outbound

This paper cites Al-Jaber, Uncertainty Relations for Some Cen- tral Potentials in N-Dimensional Space , Applied Math- ematics, 7(6), March 2016, doi:10.4236/am.2016.76047.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Al-Jaber, Uncertainty Relations for Some Cen- tral Potentials in N-Dimensional Space , Applied Math- ematics, 7(6), March 2016, doi:10.4236/am.2016.76047

Reference 13

Resolution: verified exact; raw_fallback, observed 2026-08-10T16:17:13.367224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4c6f5d3f-3f4f-4561-b6cf-915501dbd98f · outbound

This paper cites an unresolved cited work.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T16:17:12.871934Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2119f162-6153-4e22-bd2e-806fc8d7e57c · outbound

This paper cites http://dx.doi.org/ 10.1002/andp.202000335 26.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space http://dx.doi.org/ 10.1002/andp.202000335 26

Reference 15

Resolution: verified exact; doi, observed 2026-08-10T16:17:13.074269Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 40ef6658-ddb2-4ffb-aa89-27dcdf8ac905 · outbound

This paper cites Al-Jaber, Hydrogen Atom in N Dimensions , International Journal of Theoretical Physics, 37, 1289– 1298 (1998), doi:10.1023/A:1026679921970.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Al-Jaber, Hydrogen Atom in N Dimensions , International Journal of Theoretical Physics, 37, 1289– 1298 (1998), doi:10.1023/A:1026679921970

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-10T16:17:12.881746Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e2165e62-c051-4422-bb2f-53b2e8924586 · outbound

This paper cites On the connection between the radial momentum operator and the Hamiltonian in n dimensions.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space On the connection between the radial momentum operator and the Hamiltonian in n dimensions

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-10T16:17:12.887156Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 379e388a-7c75-4a35-b4d0-d24f815cfdc2 · outbound

This paper cites Supriadi, A.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Supriadi, A

Reference 18

Resolution: malformed identifier; no resolver link, observed 2026-08-10T16:17:12.892473Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0b788693-a2c6-47cd-a636-9719ae8fe7d3 · outbound

This paper cites Bransden and C.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Bransden and C

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-10T16:17:12.897955Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb0ba3ee-f9b0-4475-9c38-8a7dcf83f2b0 · outbound

This paper cites Abramowitz and I.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Abramowitz and I

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-10T16:17:12.902518Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b4bca511-c643-4bc4-ad23-4d1c1d0f3982 · outbound

This paper cites Griffiths and Darrell F.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Griffiths and Darrell F

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-10T16:17:12.907587Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69b9c941-e867-48e7-8eed-44257408cba8 · outbound

This paper cites an unresolved cited work.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-10T16:17:12.912062Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 05bc205b-1231-4469-85fc-c13a1081cfa7 · outbound

This paper cites https: //doi.org/10.13140/RG.2.2.18172.44162.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space https: //doi.org/10.13140/RG.2.2.18172.44162

Reference 23

Resolution: verified exact; raw_fallback, observed 2026-08-10T16:17:13.272741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 015a82d5-6801-41e2-9c30-9721dc37ab68 · outbound

This paper cites Indefinite Integrals of Spherical Bessel Functions.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Indefinite Integrals of Spherical Bessel Functions

Reference 24

Resolution: metadata mismatch; local_arxiv, observed 2026-08-10T16:17:13.133890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0f5e5713-9911-42c3-b81a-a4d0c8e4e0f2 · outbound

This paper cites an unresolved cited work.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:17:13.468412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a587b674-a00b-4c2c-87de-fa1a26a46035 · outbound

This paper cites https://mathworld.wolfram.com/ RegularizedHypergeometricFunction.html.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space https://mathworld.wolfram.com/ RegularizedHypergeometricFunction.html

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:13.433196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a64a9005-104a-4d59-8e23-c407024812b2 · outbound

This paper cites https://example.com/your-article-link.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space https://example.com/your-article-link

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:13.414683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 97d15c14-eb13-4e1f-bffd-0732217cd755 · outbound

This paper cites https://quantummechanics.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space https://quantummechanics

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:13.399155Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e9905b45-4910-4eec-a950-ceaa21d02939 · outbound

This paper cites an unresolved cited work.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Unresolved cited work

Reference 30

Resolution: verified exact; doi, observed 2026-08-10T16:17:13.030680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e1436890-4bb2-4ff1-a4f4-eccd58afa9fd · outbound

This paper cites Patil and K.D.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Patil and K.D

Reference 31

Resolution: verified exact; doi, observed 2026-08-10T16:17:13.006144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0e0ea683-10f6-4b33-9bb9-ba15f2ef54ac · outbound

This paper cites Pauling and E.B.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Pauling and E.B

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:13.384976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 955dae4b-29f0-4043-9a16-5470c4199d19 · outbound

This paper cites an unresolved cited work.

Radial Uncertainty Product for Spherically Symmetric Potential in Position Space Unresolved cited work

Reference 2025

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:17:13.451402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

Observation 970838df-4836-440a-aca5-4813db4a1059 · inbound

Generalized Radial Uncertainty Product for d-Dimensional Hydrogen Atom cites this paper.

Generalized Radial Uncertainty Product for d-Dimensional Hydrogen Atom Radial Uncertainty Product for Spherically Symmetric Potential in Position Space

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-09T04:37:35.674323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.