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Search: id:A122584
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| A122584 |
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Integer quantum expansion of the Mott Equation as an 8 X 8 vector Matrix Markov step 2 ( because of element doubling effect): characteristic polynomial: x=Cos[theta/2]: (-1 + 2 x^2 - x^4 - 2 x^6 + x^8). |
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+0
1
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| 1, 1, 1, 1, 2, 4, 9, 19, 41, 87, 186, 396, 845, 1801, 3841, 8189, 17462, 37232, 79389, 169275, 360937, 769603, 1640982, 3498968, 7460649, 15907905, 33919505, 72324585, 154213514, 328820508, 701124865, 1494967795, 3187632953
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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The resemblence of this equation to Ising Magntization is what made work on this. It has an interesting symmetrical vector pattern of alternasting ones and twos: {1, 0, -2, 0, 1, 0, 2, 0}
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REFERENCES
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A. Messiah, Quantum mechanics, vol. 2, p. 608-609, eq.(XIV.57), North Holland, 1969.
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FORMULA
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M = {{0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, -2, 0, 1, 0, 2, 0}}; v[1] = Table[1, {n, 1, 8}]; v[n_] := v[n] = M.v[n - 1]; a(n) = v[2*n][[1]]
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MATHEMATICA
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M = {{0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, -2, 0, 1, 0, 2, 0}}; v[1] = Table[1, {n, 1, 8}]; v[n_] := v[n] = M.v[n - 1]; a = Table[v[2*n][[1]], {n, 1, 50}]
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CROSSREFS
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Sequence in context: A052908 A036616 A136298 this_sequence A141015 A078039 A036622
Adjacent sequences: A122581 A122582 A122583 this_sequence A122585 A122586 A122587
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 19 2006
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