dorsal/arxiv
View SchemaHeisenberg's wave packet reconsidered
| Authors | J. Orlin Grabbe |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0509045 |
| URL | https://arxiv.org/abs/quant-ph/0509045 |
Abstract
This note shows that Heisenberg's choice for a wave function in his original paper on the uncertainty principle is simply a renormalized characteristic function of a stable distribution with certain restrictions on the parameters. Relaxing Heisenberg's restrictions leads to a more general formulation of the uncertainty principle. This reformulation shows quantum uncertainty can exist at a macroscopic level. These modifications also give rise to a new form of Schrodinger's wave equation as the equation of a vibrating string. Although a heat equation version can also be given, the latter shows the traditional formulation of Schrodinger's equation involves a hidden Cauchy amplitude assumption.
{
"annotation_id": "8bd9adc2-eeba-4876-97c2-8878dfb72600",
"date_created": "2026-03-02T18:02:20.657000Z",
"date_modified": "2026-03-02T18:02:20.657000Z",
"file_hash": "3af8660719f5d1782d3722b23abfd37b4a29f2c27997ab2415a58c24d0b0f9f2",
"private": false,
"record": {
"abstract": "This note shows that Heisenberg\u0027s choice for a wave function in his original\npaper on the uncertainty principle is simply a renormalized characteristic\nfunction of a stable distribution with certain restrictions on the parameters.\nRelaxing Heisenberg\u0027s restrictions leads to a more general formulation of the\nuncertainty principle. This reformulation shows quantum uncertainty can exist\nat a macroscopic level. These modifications also give rise to a new form of\nSchrodinger\u0027s wave equation as the equation of a vibrating string. Although a\nheat equation version can also be given, the latter shows the traditional\nformulation of Schrodinger\u0027s equation involves a hidden Cauchy amplitude\nassumption.",
"arxiv_id": "quant-ph/0509045",
"authors": [
"J. Orlin Grabbe"
],
"categories": [
"quant-ph"
],
"title": "Heisenberg\u0027s wave packet reconsidered",
"url": "https://arxiv.org/abs/quant-ph/0509045"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "cd73bec4-168c-45a4-bc65-320b1b3d78e5",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}