On the (Non)Equivalence of the Schrödinger and Heisenberg Pictures of Quantum Mechanics

2014/04/27 by Maurice A. de Gosson, de Gosson, Maurice A. · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #NA #Operator Algebras (math.OA) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math-ph #math.MP #math.OA #quant-ph

paper · pdf · doi:10.48550/arxiv.1404.6775

Funded by Austrian Research grant FWF P20442-N13

arxiv created 2014/04/27 · openalex publication_date 2014/04/27 · arxiv updated 2014/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this short Note is to show that the Schrödinger and Heisenberg pictures of quantum mechanics are not equivalent unless one uses a quantization rule clearly stated by Born and Jordan in their famous 1925 paper. This rule is sufficient and necessary to ensure energy conservation in Heisenberg's matrix mechanics. It follows, in particular, that Schrödinger and Heisenberg mechanics are not equivalent if one quantizes observables using the Weyl prescription.

Cited by

• Born--Jordan Quantization and the Equivalence of Matrix and Wave Mechanics

Related

• Born--Jordan Quantization and the Equivalence of Matrix and Wave Mechanics
• The Heisenberg versus the Schrodinger picture in quantum field theory
• Short-Time Propagators and the Born--Jordan Quantization Rule
• Equivalence Relations in Quantum Theory: An Objective Account of Bases and Factorizations
• The Quantum Formalism Revisited