Quantum Representation of Classical Dynamics

Technical Report · Fri Dec 21 04:00:00 EST 2018

DOI:https://doi.org/10.2172/1498458· OSTI ID:1498458

Joseph, Ilon ^[1]

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1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

A constructive proof is given to show that there is an exact embedding of a classical system of N ordinary differential equations (ODEs) within a quantum mechanical system corresponding to a classical phase space of dimension 2N. Doubling the classical phase space allows one to express any set of ODEs through a classical Hamiltonian that is a sum over a set of constraints. The Lagrange multipliers that enforce the constraints are canonically conjugate to the dependent variables of the original ODE and satisfy equations that ensure that the evolution of the system is symplectic. For the quantized system on extended phase space, Heisenberg’s uncertainty principle is satisfied by each variable and its canonically conjugate momentum, the Lagrange multiplier. However, there is no uncertainty in a simultaneous measurement for any of the variables of the original ODE. Hence,there is complete fidelity for the quantum representation of the classical system.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: AC52-07NA27344
• OSTI ID: 1498458
• Report Number(s): LLNL-TR--765903; 954690
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
classical mechanics
quantum computing
quantum mechanics
quantum-classical correspondence