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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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