Lecture25-1

Lecture25-1 - CHEM 356 Lecture 25 Fall 2009 1 Electron Spin...

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Unformatted text preview: CHEM 356, Lecture 25, Fall 2009 1 Electron Spin Angular Momentum. II. ∙ Goudsmit and Uhlenbeck (1926): postulated that the electron has an intrinsic angular momentum of magnitude ℏ / 2, which they proposed to call (electron) ‘spin’. = 1 2 −→ − 1 2 ≤ ≤ + 1 2 ∙ Representation of the angular momentum states of spin– 1 2 particles is accomplished by employing a 2D vector space: let us choose as basis vectors the primitive unit vectors (identified, as is traditional, by ∣ ? ⟩ and ∣ ? ⟩ ) ∣ ? ⟩ ≡ ( 1 ) ; ∣ ? ⟩ ≡ ( 1 ) . ∙ Pauli (1928) : proposed the matrix representation for the spin operators that is used today, in terms of 2 × 2 matrices identified as S ? = ℏ 2 ( 1 1 ) ; S ? = ℏ 2 ( − ) ; S ? = ℏ 2 ( 1 − 1 ) ; from which we may obtain also the form for S 2 as S 2 = S 2 ? + S 2 ? + S 2 ? = 3 4 ℏ 2 ˆ 1 . ∙ Vector Model: the spin vector has length √ 3 ℏ / 2, which is greater than ℏ / 2 because = ± 1 2 ℏ represents the projection of the vector along the ? –axis. For ? giving eigenvalue + 1 2 ℏ , the spin vector lies somewhere on the surface of a cone such that the projection of S along the ? –axis has the value + 1 2 ℏ . The spin vector S can thus be thought of as precessing around the ? –axis. CHEM 356, Lecture 25, Fall 2009 2 ∙ Every angular momentum has a magnetic moment associated with it: we can write the relation between the associated magnetic moment and the angular momentum J as (m) ∝ J , or as...
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Lecture25-1 - CHEM 356 Lecture 25 Fall 2009 1 Electron Spin...

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