dorsal/arxiv
View SchemaQuantum Mechanics from the Hamilton-Jacobi Point of View
| Authors | Alexander Jurisch |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612217 |
| URL | https://arxiv.org/abs/quant-ph/0612217 |
Abstract
In this article, we develop quantum mechanics upon the framework of the quantum mechanical Hamilton-Jacobi theory. We will show, that the Schroedinger point of view and the Hamilton-Jacobi point of view are fully equivalent in their description of physical systems, but differ in their descriptive manner. As a main result, a wave function in Hamilton-Jacobi theory can be decomposed into travelling waves in any point in space, not only asymptotically. The well known WKB-theory will be a special result of the more general theory, we will develop below. By the example of the linear potential and the harmonic oscillator, we will discuss quantum mechanics from the Hamilton-Jacobi point of view. Soft boundary value problems as the connection problem can be solved exactely. Quantizised energies and Maslov-indices can be calculated directely without orthonormalizing wave-functions. Also, we will focus on trajectory themes, which, in contrast to the Schroedinger point of view, follow naturally from the quantum mechanical action function.
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"abstract": "In this article, we develop quantum mechanics upon the framework of the\nquantum mechanical Hamilton-Jacobi theory. We will show, that the Schroedinger\npoint of view and the Hamilton-Jacobi point of view are fully equivalent in\ntheir description of physical systems, but differ in their descriptive manner.\nAs a main result, a wave function in Hamilton-Jacobi theory can be decomposed\ninto travelling waves in any point in space, not only asymptotically. The well\nknown WKB-theory will be a special result of the more general theory, we will\ndevelop below. By the example of the linear potential and the harmonic\noscillator, we will discuss quantum mechanics from the Hamilton-Jacobi point of\nview. Soft boundary value problems as the connection problem can be solved\nexactely. Quantizised energies and Maslov-indices can be calculated directely\nwithout orthonormalizing wave-functions. Also, we will focus on trajectory\nthemes, which, in contrast to the Schroedinger point of view, follow naturally\nfrom the quantum mechanical action function.",
"arxiv_id": "quant-ph/0612217",
"authors": [
"Alexander Jurisch"
],
"categories": [
"quant-ph"
],
"title": "Quantum Mechanics from the Hamilton-Jacobi Point of View",
"url": "https://arxiv.org/abs/quant-ph/0612217"
},
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"execution_id": "83e59c65-c60b-4319-bc77-2d169f43db83",
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