Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

A discussion on the eigenvalues of sum operators in the Hilbert space

Document Type : Original Article

Authors
1 Department of Physics, Iran University of Science and Technology, Tehran, 16846-13214, Narmak, Iran
2 Department of Physics, Amirkabir University of Technology (Tehran Polytechnic ), P.O.Box: 15875-4413,Tehran, Iran
Abstract
In this paper, we present rigorous proofs and counterexamples showing that the notion of partiality (reductionism) does not apply to operators in Hilbert space. We argue that the classical concepts of partiality and totality (holism) are fundamentally incompatible with the structure of quantum mechanics. This claim is supported across different interpretations of quantum theory, including cases involving nonlinear operators. Our analysis highlights the limitations of classical intuition in operator algebra and provides a refined understanding of eigenvalue behavior in quantum systems.
Keywords
Subjects

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Volume 3, Issue 2
Spring 2026
Pages 66-68

  • Receive Date 08 May 2026
  • Accept Date 15 May 2026
  • First Publish Date 15 May 2026
  • Publish Date 01 May 2026