dorsal/arxiv
View SchemaSuperseded version of the WKB approximation and explanation of emergence of classicality
| Authors | Wang Guowen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612203 |
| URL | https://arxiv.org/abs/quant-ph/0612203 |
Abstract
Regarding the limit hbar-->0 as the classical limit of quantum mechanics seems to be silly because hbar is a definite constant of physics, but it was successfully used in the derivation of the WKB approximation. A superseded version of the WKB approximation is proposed in the classical limit alpha-->0 where alpha=m/M is the screening parameter of an object in which m is the mass of the effective screening layer and M the total mass. This version is applicable to not only approximate solution of Schrodinger equation of a quantum particle but also that of a nanoparticle. Moreover, the version shows that the quantization rules for nanoparticles can be achieved by substituting alpha times hbar for hbar in the Bohr-Sommerfeld quantization rules of the old quantum theory. Most importantly, the version helps clarify the essential difference between classical and quantum realities and understand the transition from quantum to classical mechanics as well as quantum mechanics itself.
{
"annotation_id": "3d16d607-5a97-4f47-a5af-8fadaf0fb0f9",
"date_created": "2026-03-02T18:02:34.378000Z",
"date_modified": "2026-03-02T18:02:34.378000Z",
"file_hash": "42b6ef26972d68b2d8f2587b8b3d8232cbad694154566cdd3e374ed8af71b753",
"private": false,
"record": {
"abstract": "Regarding the limit hbar--\u003e0 as the classical limit of quantum mechanics\nseems to be silly because hbar is a definite constant of physics, but it was\nsuccessfully used in the derivation of the WKB approximation. A superseded\nversion of the WKB approximation is proposed in the classical limit alpha--\u003e0\nwhere alpha=m/M is the screening parameter of an object in which m is the mass\nof the effective screening layer and M the total mass. This version is\napplicable to not only approximate solution of Schrodinger equation of a\nquantum particle but also that of a nanoparticle. Moreover, the version shows\nthat the quantization rules for nanoparticles can be achieved by substituting\nalpha times hbar for hbar in the Bohr-Sommerfeld quantization rules of the old\nquantum theory. Most importantly, the version helps clarify the essential\ndifference between classical and quantum realities and understand the\ntransition from quantum to classical mechanics as well as quantum mechanics\nitself.",
"arxiv_id": "quant-ph/0612203",
"authors": [
"Wang Guowen"
],
"categories": [
"quant-ph"
],
"title": "Superseded version of the WKB approximation and explanation of emergence of classicality",
"url": "https://arxiv.org/abs/quant-ph/0612203"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "023f20da-ffd7-4fe6-82b1-a96700bb47da",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}