2024/05/07 by Frank Wilczek, Wilczek, Frank, Zara Yu +1
Decision Sciences · #FOS: Physical sciences #Quantum Physics (quant-ph) #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2405.04493
openalex publication_date 2024/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
Postulating the identification of ψ^*(x, t) ψ(x,t) with a physical probability density is unsatisfactory conceptually and overly limited practically. For electrons, there is a simple, calculable relativistic correction proportional to ∇ ψ^* ⋅ ∇ ψ. In particular, zeroes of the wave function do not indicate vanishing probability density of presence. We derive a correction of this kind from a Lagrangian, in a form suitable for wide generalization and use in effective field theories. Thus we define a large new class of candidate models for (quasi-)particles and fields, featuring modified \it kinetic\/ terms. We solve for the stationary states and energy spectrum in some representative problems, finding striking effects including the emergence of negative effective mass at high energy and of localization by energy. \endabstract