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40 lines
921 B
Plaintext
40 lines
921 B
Plaintext
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reestablish fundamental brakets
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spin Z operators
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raising/lowering operators (lowering erased before pic)
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commutations relations (erased before pic)
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Now setup a two-spin system
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(pic) Look at general operator expressions ?? in different spaces ??
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Take direct product of A and B
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(pic) Developed 𝐒 using raising lowering operators
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(pic: last y should be an x) Proved this.
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(pic x2) Still missing a 1/2 somewhere! But moving on to see proper solutions of direct product.
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Eigenvalues are
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𝐒² = ħ² S(S+1) = ⎧ 2ħ²
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⎨
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⎩ 0ħ²
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𝐒 = ⎧ 1 (3 eigenstates)
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⎨
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⎩ 0 (1 eigenstate)
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(pic) Plugging back to direct product matrix
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(pic) FOUND PROBLEM of -1/2 from the up/down raising/lowering operator interactions
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(pic) finished diagonalizing operator product
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