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A solution (Dirac electron in crossed, constant electric and magnetic fields) that has found a problem (relativistic quantized Hall effect)

Michael Martin Nieto, Philip L. Taylor

The exactly solvable Dirac electron in crossed, constant electric and magnetic fields represents the relativistic quantized Hall effect. The solution allows one to show that there are no relativistic quantum-mechanical corrections to the ordinary quantized Hall effect.

American Journal of PhysicsMar 1, 198514 citations

Spin Quantization and the Relativistically Spinning Sphere

Malcolm H. Mac Gregor

Springer eBooksJan 1, 19920 citations

Canonical quantization of a Dirac spin particle in an external magnetic field

G. V. Grigoryan, R. P. Grigoryan, E. Yankovsky

Journal of Experimental and Theoretical PhysicsJan 1, 19931 citation

Quasi-classical theory of cyclotron resonance with accounting for dissipation

С. В. Сазонов

Abstract Based on the quasi-classical version of the canonical Caldirola–Kanai quantization, non-relativistic cyclotron resonance in a dissipative medium is studied. The corresponding particle propagator in the coordinate representation is found. It is shown that the combined effect of dissipation and a constant magnetic field reduces to the suppression of the quantum properties of a charged particle. In turn, a time-varying electric field that causes cyclotron resonance does not exhibit similar properties and does not affect the uncertainties of the particle coordinates.Abstract Based on the quasi-classical version of the canonical Caldirola–Kanai quantization, non-relativistic cyclotron resonance in a dissipative medium is studied. The corresponding particle propagator in the coordinate representation is found. It is shown that the combined effect of dissipation and a constant magnetic field reduces to the suppression of the quantum properties of a charged particle. In turn, a time-varying electric field that causes cyclotron resonance does not exhibit similar properties and does not affect the uncertainties of the particle coordinates.

Laser Physics LettersMar 27, 20240 citations

Toward a Causal Interpretation of the Relativistic Quantum Mechanics of a Spinning Particle

Nicola Cufaro Petroni

NATO ASI series. Series B : PhysicsJan 1, 19870 citations

Equivalence of classical Klein-Gordon field theory to correspondence-principle first quantization of the spinless relativistic free particle

Steven Kenneth Kauffmann

It has recently been shown that the classical electric and magnetic fields which satisfy the source-free Maxwell equations can be linearly mapped into the real and imaginary parts of a transverse-vector wave function which in consequence satisfies the time-dependent Schroedinger equation whose Hamiltonian operator is physically appropriate to the free photon. The free-particle Klein-Gordon equation for scalar fields modestly extends the classical wave equation via a mass term. It is physically untenable for complex-valued wave functions, but has a sound nonnegative conserved-energy functional when it is restricted to real-valued classical fields. Canonical Hamiltonization and a further canonical transformation maps the real-valued classical Klein-Gordon field and its canonical conjugate into the real and imaginary parts of a scalar wave function (within a constant factor) which in consequence satisfies the time-dependent Schroedinger equation whose Hamiltonian operator has the natural correspondence-principle relativistic square-root form for a free particle, with a mass that matches the Klein-Gordon field theory's mass term. Quantization of the real-valued classical Klein-Gordon field is thus second quantization of this natural correspondence-principle first-quantized relativistic Schroedinger equation. Source-free electromagnetism is treated in a parallel manner, but with the classical scalar Klein-Gordon field replaced by a transverse vector potential that satisfies the classical wave equation. This reproduces the previous first-quantized results that were based on Maxwell's source-free electric and magnetic field equations.It has recently been shown that the classical electric and magnetic fields which satisfy the source-free Maxwell equations can be linearly mapped into the real and imaginary parts of a transverse-vector wave function which in consequence satisfies the time-dependent Schroedinger equation whose Hamiltonian operator is physically appropriate to the free photon. The free-particle Klein-Gordon equation for scalar fields modestly extends the classical wave equation via a mass term. It is physically untenable for complex-valued wave functions, but has a sound nonnegative conserved-energy functional when it is restricted to real-valued classical fields. Canonical Hamiltonization and a further canonical transformation maps the real-valued classical Klein-Gordon field and its canonical conjugate into the real and imaginary parts of a scalar wave function (within a constant factor) which in consequence satisfies the time-dependent Schroedinger equation whose Hamiltonian operator has the natural correspondence-principle relativistic square-root form for a free particle, with a mass that matches the Klein-Gordon field theory's mass term. Quantization of the real-valued classical Klein-Gordon field is thus second quantization of this natural correspondence-principle first-quantized relativistic Schroedinger equation. Source-free electromagnetism is treated in a parallel manner, but with the classical scalar Klein-Gordon field replaced by a transverse vector potential that satisfies the classical wave equation. This reproduces the previous first-quantized results that were based on Maxwell's source-free electric and magnetic field equations.

arXiv:1012.5120Dec 14, 20101 citation

Relativistic Corrections to the Quantization of a Classical Spinning Particle with Constant Electric and Magnetic Fields

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Relativistic Corrections to the Quantization of a Classical Spinning Particle with Constant Electric and Magnetic Fields

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