dorsal/arxiv
View SchemaFrom Classical Hamiltonian Flow to Quantum Theory: Derivation of the Schroedinger Equation
| Authors | Gerhard Groessing |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0311109 |
| URL | https://arxiv.org/abs/quant-ph/0311109 |
| DOI | 10.1023/B:FOPL.0000035669.03595.ce |
| Journal | Foundations of Physics Letters 17, 4 (2004) 343 - 362. |
Abstract
It is shown how the essentials of quantum theory, i.e., the Schroedinger equation and the Heisenberg uncertainty relations, can be derived from classical physics. Next to the empirically grounded quantisation of energy and momentum, the only input is given by the assumption of fluctuations in energy and momentum to be added to the classical motion. Extending into the relativistic regime for spinless particles, this procedure leads also to a derivation of the Klein-Gordon equation. Comparing classical Hamiltonian flow with quantum theory, then, the essential difference is given by a vanishing divergence of the velocity of the probability current in the former, whereas the latter results from a much less stringent requirement, i.e., that only the average over fluctuations and positions of the average divergence be identical to zero.
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"abstract": "It is shown how the essentials of quantum theory, i.e., the Schroedinger\nequation and the Heisenberg uncertainty relations, can be derived from\nclassical physics. Next to the empirically grounded quantisation of energy and\nmomentum, the only input is given by the assumption of fluctuations in energy\nand momentum to be added to the classical motion. Extending into the\nrelativistic regime for spinless particles, this procedure leads also to a\nderivation of the Klein-Gordon equation. Comparing classical Hamiltonian flow\nwith quantum theory, then, the essential difference is given by a vanishing\ndivergence of the velocity of the probability current in the former, whereas\nthe latter results from a much less stringent requirement, i.e., that only the\naverage over fluctuations and positions of the average divergence be identical\nto zero.",
"arxiv_id": "quant-ph/0311109",
"authors": [
"Gerhard Groessing"
],
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"quant-ph"
],
"doi": "10.1023/B:FOPL.0000035669.03595.ce",
"journal_ref": "Foundations of Physics Letters 17, 4 (2004) 343 - 362.",
"title": "From Classical Hamiltonian Flow to Quantum Theory: Derivation of the Schroedinger Equation",
"url": "https://arxiv.org/abs/quant-ph/0311109"
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