Diagonal Representation for a Generic Matrix Valued Quantum Hamiltonian
arXiv:0801.0940 · doi:10.1140/epjc/s10052-009-1155-3
Abstract
A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a running variable are introduced. This method leads to a formal compact expression for the diagonal Hamiltonian which can be expanded in a power series of the Planck constant. In particular, we provide an explicit expression for the diagonal representation of a generic Hamiltonian to the second order in the Planck constant. This last result is applied, as a physical illustration, to Dirac electrons and neutrinos in external fields.
Significant revision, typos corrected and references added
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Cited by in corpus (13)
- General method of the relativistic Foldy-Wouthuysen transformation and proof of validity of the Foldy-Wouthuysen Hamiltonian
- Position and spin in relativistic quantum mechanics
- General properties of the Foldy-Wouthuysen transformation and applicability of the corrected original Foldy-Wouthuysen method
- Relativistic quantum dynamics of twisted electron beams in arbitrary electric and magnetic fields
- Position, spin and orbital angular momentum of a relativistic electron
- Comparative analysis of direct and "step-by-step" Foldy-Wouthuysen transformation methods
- General relativity effects in precision spin experimental tests of fundamental symmetries
- Validation of the Eriksen Method of the Exact Foldy-Wouthuysen Representation
- Appearance of Gauge Fields and Forces beyond the adiabatic approximation
- Dirac Particles in a Gravitational Field
- Appearance of Gauge Fields and Forces beyond the adiabatic approximation
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- Phase space curvature in spin-orbit coupled ultracold atom systems