From Classical Hamiltonian Flow to Quantum Theory: Derivation of the Schrödinger Equation
Gerhard Grössing,
Austrian Institute for Nonlinear Studies,
Parkgasse 9, A-1030 Vienna, Austria
Abstract:
It is shown how the essentials of quantum theory, i.e., the Schrödinger 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.
To download the article click on the link below:
https://arxiv.org/ftp/quant-ph/papers/0311/0311109.pdf
Austrian Institute for Nonlinear Studies,
Parkgasse 9, A-1030 Vienna, Austria
Abstract:
It is shown how the essentials of quantum theory, i.e., the Schrödinger 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.
To download the article click on the link below:
https://arxiv.org/ftp/quant-ph/papers/0311/0311109.pdf
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