New exact solutions of the Dirac equation

1970 ◽  
Vol 48 (16) ◽  
pp. 1935-1937 ◽  
Author(s):  
Lui Lam
Keyword(s):  
Dirac Equation ◽  
Magnetic Fields ◽  
Exact Solutions ◽  
New Exact Solutions ◽  
Electric And Magnetic Fields ◽  
Dirac Electron ◽  
Klein Gordon ◽  
Special Case

Exact solutions of a Dirac electron in constant crossed electric and magnetic fields are found and given explicitly. The case of Klein–Gordon particles is shown to be a special case of ours.

INVARIANT SOLUTION OF THE DIRAC EQUATION IN THE CROSSED ELECTRIC AND MAGNETIC FIELDS $ (H \mathclose{>} E) $

2019 ◽  
Vol 53 (2 (249)) ◽  
pp. 138-141
Author(s):  
R.G. Petrosyan ◽  
M.A. Davtyan
Keyword(s):  
Dirac Equation ◽  
Magnetic Fields ◽  
Harmonic Oscillator ◽  
Invariant Solution ◽  
Charged Particles ◽  
Invariant Solutions ◽  
Quantum Harmonic Oscillator ◽  
Electric And Magnetic Fields

In the article exact analytical and invariant solutions for both spinless and half-spin relativistic charged particles in crossed constant electric and magnetic fields, when $ H \mathclose{>} E $ have been found. It is shown that in both cases the problem reduces to that of quantum harmonic oscillator.

Relativistic charge currents in oblique electric and magnetic fields

1991 ◽  
Vol 45 (3) ◽  
pp. 415-425
Author(s):  
Fulvio Melia ◽  
Marco Fatuzzo
Keyword(s):  
Magnetic Fields ◽  
Plasma Heating ◽  
Field Configuration ◽  
Anisotropic Conductivity ◽  
Electric And Magnetic Fields ◽  
Magnetic Tearing ◽  
Sudden Release ◽  
Transient Events ◽  
Special Case ◽  
Theoretical Standpoint

Runaway processes on neutron stars leading to the sudden release of large quantities of energy (up to of order 1040 erg) on time scales as short as a fraction of a second involve plasma heating and particle acceleration in superstrong magnetic fields H (of order 1012 G). These transient events are interesting from a theoretical standpoint because they require knowledge of particle transport properties in low-density plasmas (εe ≲ 1025 cm−3) threaded by both electric (E) and magnetic fields. The evaluation of matrix elements involving solutions to the Dirac equation for such a field configuration is often difficult and sometimes impossible, since no completely normalized wave function has yet been found. Here it is shown that, in the special case of E/H ≲ 10−4, a simplification of the overlap integrals permits an analytical integration that yields explicit expressions for the relativistic charge currents needed in the computation of the anisotropic conductivity tensor when E.H ≠ 0. The application of these results to the evaluation of the conductivity is briefly discussed. Among other things, this work is relevant to a theory of resistive magnetic tearing instabilities in a quantizing field.

New exact solutions of the dirac equation. XII

1985 ◽  
Vol 28 (1) ◽  
pp. 70-74
Author(s):  
V. G. Bagrov ◽  
M. D. Noskov ◽  
V. N. Shapovalov
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
New Exact Solutions
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