de Broglie-Bohm guidance equations for arbitrary Hamiltonians
Abstract
In a pilot-wave theory, an individual closed system is described by a wavefunction ψ(q) and configuration q. The evolution of the wavefunction and configuration are respectively determined by the Schrödinger and guidance equations. The guidance equation states that the velocity field for the configuration is given by the quantum current divided by the density |ψ(q)|2. We present the currents and associated guidance equations for any Hamiltonian given by a differential operator. These are derived directly from the Schrödinger equation, and also as Noether currents arising from a global phase symmetry associated with the wavefunction in configuration space.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- January 2009
- DOI:
- 10.1088/1751-8113/42/3/035301
- arXiv:
- arXiv:0808.0290
- Bibcode:
- 2009JPhA...42c5301S
- Keywords:
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- Quantum Physics;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory
- E-Print:
- 22 pages, no figures, LaTex