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.
Jarollahi,H and Jafari Matehkolaee,M . (2026). A discussion on the eigenvalues of sum operators in the Hilbert space. Transactions in Theoretical and Mathematical Physics, (), 66-68. doi: 10.30511/ttmp.2026.2088274.1075
MLA
Jarollahi,H , and Jafari Matehkolaee,M . "A discussion on the eigenvalues of sum operators in the Hilbert space", Transactions in Theoretical and Mathematical Physics, , , 2026, 66-68. doi: 10.30511/ttmp.2026.2088274.1075
HARVARD
Jarollahi H, Jafari Matehkolaee M. (2026). 'A discussion on the eigenvalues of sum operators in the Hilbert space', Transactions in Theoretical and Mathematical Physics, (), pp. 66-68. doi: 10.30511/ttmp.2026.2088274.1075
CHICAGO
H Jarollahi and M Jafari Matehkolaee, "A discussion on the eigenvalues of sum operators in the Hilbert space," Transactions in Theoretical and Mathematical Physics, (2026): 66-68, doi: 10.30511/ttmp.2026.2088274.1075
VANCOUVER
Jarollahi H, Jafari Matehkolaee M. A discussion on the eigenvalues of sum operators in the Hilbert space. TTMP. 2026;():66-68. doi: 10.30511/ttmp.2026.2088274.1075
