Volume 22: Pages 173-178, 2009

Hidden statistics of Schrödinger equation

Michail Zak ¹

¹Advance Computing Algorithms and IVHM Group, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA

Based on the Madelung version of Schrödinger equation, the origin of randomness in quantum mechanics has been traced down to instability generated by quantum potential at the point of departure from a deterministic state. The instability triggered by failure of the Lipchitz condition splits the solution into a continuous set of random samples representing a hidden statistics of Schrödinger equation, i.e., the transitional stochastic process as a “bridge” to quantum world. The hidden statistics confirms the uncertainty principle, and it justifies the belief by most physicists that particle trajectories do not exist, although, to be more precise, it demonstrates that deterministic trajectories exist but they are highly unstable. Unlike the Schrödinger equation that describes probabilities, its hidden statistics simulates probabilities. A dimensionless parameter characterizing the hidden statistics has been introduced. This parameter can be exploited as a similarity criterion, and that allows one to choose an appropriate scale that is not necessarily quantum, for simulation. Following the proposed reinterpretation of quantum formalism, implementation of quantum computing and quantum information processing on a classical scale has been discussed.

Keywords: Origin of Randomness, Lipchitz Condition, Quantum Potential, Similarity Parameter, Nonquantum-Scale Simulation, Quantum Computing

Received: December 28, 2008; Accepted: April 2, 2009; Published Online: April 30, 2009