Revivals and quantum carpets for the relativistic Schrödinger equation

• URL: http://arxiv.org/abs/2511.05200v1
• Date: Fri, 07 Nov 2025 12:39:00 GMT
• Title: Revivals and quantum carpets for the relativistic Schrödinger equation
• Authors: Benoît Zumer, Florent Daem, Alexandre Matzkin,
• Abstract summary: We investigate wavepacket dynamics for a relativistic particle in a box evolving according to the Schr"odinger equation.<n>We obtain expressions for the wavepacket revival times and explore the corresponding quantum carpets.<n>We analyze level spacing statistics as the dynamics goes from the non-relativistic regime to the ultra-relativistic limit.
• Score: 41.99844472131922
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate wavepacket dynamics for a relativistic particle in a box evolving according to the relativistic Schr\"odinger (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.

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