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March 5, 20260 citationsOpen Access

ELECTRON SPIN IN THE REPRESENTATION WHICH MAKES σ ᵦ DIAGONAL AND IN THE REPRESENTATION THAT MAKES σ ₓ DIAGONAL

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DDDr. Palash Das

Key Points

  • This research aims to calculate and compare the density matrices of an electron spin in two different representations where the Pauli matrices are diagonal.
  • Calculated the density matrix of an electron spin in the representation that makes σ_z diagonal.
  • Performed similar calculations for the representation that makes σ_x diagonal.
  • Calculated ensemble averages of expectation values for both representations.
  • Both representations yield the same ensemble average of the expectation value, confirming their equivalence.
  • Demonstrated that the usage of different diagonal representations does not change the fundamental outcome.

Abstract

We calculate the density matrix of an electron spin in the representation that makes diagonal and hence calculate the ensemble average of the expectation value of .We make the same scheme in the representation that makes diagonal and show that the ensemble average of the expectation value of , resulting from this representation is precisely the same as the initial one, where are Pauli’s spin matrices and is the z-component of the intrinsic magnetic moment of the electron. We then conclude accordingly.

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Cite This Study

Dr. Palash Das (2026) studied this question.

synapsesocial.com/papers/69a91e57d6127c7a504c23behttps://doi.org/10.5281/zenodo.18847085
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Solving one-body ensemble N-representability problems with spin2025
  2. 2Generalized spin in the variational determination of two-electron reduced density matrices within the doubly occupied configuration interaction framework2025
  3. 3Spin Alignment, Tensor Polarizabilities, and Local Equilibrium for Spin-1 Particles2026 · 2 citations
  4. 4Spin alignment of vector mesons in local equilibrium by Zubarev’s approach2025
  5. 5Description of the Electron in the Electromagnetic Field: The Dirac Type Equation and the Equation for the Wave Function in Spinor Coordinate Space2025