Relativistic Wave Equations: An Operational Approach

Abstract

The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential equations, such as relativistic Schrödinger, Klein-Gordon and Dirac. We discuss the free particle hypotheses and those relevant to particles subject to non-trivial potentials. In the latter case we will show how the proposed method leads to easily implementable numerical algorithms.

References in corpus (10)

• Understanding individual human mobility patterns
• The Magnus expansion and some of its applications
• Quantum simulation of the Dirac equation
• Exact and explicit probability densities for one-sided Levy stable distributions
• Photonic analogue of Zitterbewegung in binary waveguide arrays
• Levy stable two-sided distributions: exact and explicit densities for asymmetric case
• The Salpeter equation and probability current in the relativistic Hamiltonian quantum mechanics
• The relativistic massless harmonic oscillator
• Relativistic equations with fractional and pseudo-differential operators
• Zitterbewegung by Quantum Field Theory Considerations

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• Quantum mechanical Gaussian wavepackets of single relativistic particles