The position-momentum commutator as a generalized function: resolution of the apparent discrepancy between continuous and discrete bases

DOI10.1007/s10701-023-00697-8zbMath1528.81170OpenAlexW4376646858MaRDI QIDQ6170733

Timothy B. Boykin

Publication date: 13 July 2023

Published in: Foundations of Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10701-023-00697-8

zbMATH Keywords

incompletenesscommutatorDirac delta functiondiscrete basis

Mathematics Subject Classification ID

Operations with distributions and generalized functions (46F10) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) (26B20) Gödel numberings and issues of incompleteness (03F40) Special bases (entangled, mutual unbiased, etc.) (81P55) Paracontrolled distributions and alternative approaches (60L40)

Cites Work

• Unnamed Item
• Derivatives of the Dirac delta function by explicit construction of sequences
• The discretized Schrödinger equation and simple models for semiconductor quantum wells
• Digital orbitals: connecting the tight-binding and plane-wave approaches through sampled-real-space models

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