dorsal/arxiv
View SchemaOn an Elementary Derivation of the Hamilton-Jacobi Equation from the Second Law of Newton
| Authors | A. Granik |
|---|---|
| Categories | |
| ArXiv ID | physics/0309059 |
| URL | https://arxiv.org/abs/physics/0309059 |
Abstract
It is shown that for a relativistic particle moving in an electromagnetic field its equations of motion written in a form of the second law of Newton can be reduced with the help of elementary operations to the Hamilton-Jacobi equation. The derivation is based on a possibility of transforming the equation of motion to a completely antisymmetric form. Moreover, by perturbing the Hamilton-Jacobi equation we obtain the principle of least action.\ The analogous procedure is easily extended to a general relativistic motion of a charged relativistic particle in an electromagnetic field. It sis also shown that the special-relativistic Hamilton-Jacobi equation for a free particle allows one to easily demonstrate the wave-particle duality inherent to this equation and, in addition, to obtain the operators of the four-momentum whose eigenvalues are the classical four-momentum
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"abstract": "It is shown that for a relativistic particle moving in an electromagnetic\nfield its equations of motion written in a form of the second law of Newton can\nbe reduced with the help of elementary operations to the Hamilton-Jacobi\nequation. The derivation is based on a possibility of transforming the equation\nof motion to a completely antisymmetric form. Moreover, by perturbing the\nHamilton-Jacobi equation we obtain the principle of least action.\\\n The analogous procedure is easily extended to a general relativistic motion\nof a charged relativistic particle in an electromagnetic field. It sis also\nshown that the special-relativistic Hamilton-Jacobi equation for a free\nparticle allows one to easily demonstrate the wave-particle duality inherent to\nthis equation and, in addition, to obtain the operators of the four-momentum\nwhose eigenvalues are the classical four-momentum",
"arxiv_id": "physics/0309059",
"authors": [
"A. Granik"
],
"categories": [
"physics.gen-ph",
"physics.ed-ph"
],
"title": "On an Elementary Derivation of the Hamilton-Jacobi Equation from the Second Law of Newton",
"url": "https://arxiv.org/abs/physics/0309059"
},
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