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Abstract The time‐dependent Schrödinger equation can be rewritten so that its interpretation is no longer probabilistic. Two well‐known and related reformulations are Bohmian mechanics and quantum hydrodynamics. In these formulations, quantum particles follow real, deterministic trajectories influenced by a quantum force. Generally, trajectory methods are not applied to electronic structure calculations as they predict that the electrons in a ground‐state, real, molecular wavefunction are motionless. However, a spin‐dependent momentum can be recovered from the nonrelativistic limit of the Dirac equation. Therefore, we developed new, spin‐dependent equations of motion for the quantum hydrodynamics of electrons in molecular orbitals. The equations are based on a Lagrange multiplier, which constrains each electron to an isosurface of its molecular orbital, as required by the spin‐dependent momentum. Both the momentum and the Lagrange multiplier provide a unique perspective on the properties of electrons in molecules.
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Everettian Mechanics with Hyperfinitely Many Worlds
Abstract The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different outcomes are associated with possibly infinitesimal probabilities. One can also prove hyperfinite formulations of Everett’s limiting relative-frequency and randomness properties, theorems he considered central to his formulation of quantum mechanics. Finally, this model provides an intuitive framework in which to consider no-collapse formulations of quantum mechanics more generally.
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- Award ID(s):
- 2054477
- PAR ID:
- 10369059
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Erkenntnis
- Volume:
- 89
- Issue:
- 4
- ISSN:
- 0165-0106
- Format(s):
- Medium: X Size: p. 1367-1386
- Size(s):
- p. 1367-1386
- Sponsoring Org:
- National Science Foundation
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