Revivals and quantum carpets for the relativistic Schrödinger equation

Abstract

We investigate wavepacket dynamics for a relativistic particle in a box evolving according to the relativistic Schrödinger (also known as the Salpeter) equation. We derive the solutions for an infinite well -- which contrary to the standard relativistic wave equations (such as the Klein-Gordon or Dirac equations) -- are well defined, and use these solutions to construct wavepackets. We obtain expressions for the wavepacket revival times and explore the corresponding quantum carpets (the space-time probability density plots) for different dynamical regimes. We further analyze level spacing statistics as the dynamics goes from the non-relativistic regime to the ultra-relativistic limit.

References in corpus (5)

• One-Dimensional Semirelativistic Hamiltonian with Multiple Dirac Delta Potentials
• Causal evolution of wave packets
• General pseudo self-adjoint boundary conditions for a 1D KFG particle in a box
• Beyond the light-cone propagation of relativistic wavefunctions: numerical results
• Effects of superradiance on relativistic Foldy-Wouthuysen densities