Solution9.nb

Solution9.nb - Homework 9, Problem 2 ke = Table@ [email protected] j, 2,...

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Homework 9, Problem 2 ke = Table @ If @ i ã j, 2, If @ Abs @ i - j D ã 1, - 1, 0 DD , 8 i, 61 < , 8 j, 61 <D ê H 0.1 * 0.1 * 2 L * 1.0; udiag = Table @ - 2 ê Sqrt @H i * 0.1 - 3.1 L ^2 + 1 D , 8 i, 61 <D 8 - 0.632456, - 0.651981, - 0.672673, - 0.694629, - 0.717958, - 0.742781, - 0.769231, - 0.797452, - 0.827606, - 0.859867, - 0.894427, - 0.931493, - 0.971286, - 1.01404, - 1.06, - 1.1094, - 1.16248, - 1.21942, - 1.28037, - 1.34535, - 1.41421, - 1.48659, - 1.56174, - 1.63846, - 1.71499, - 1.78885, - 1.85695, - 1.91565, - 1.96116, - 1.99007, - 2., - 1.99007, - 1.96116, - 1.91565, - 1.85695, - 1.78885, - 1.71499, - 1.63846, - 1.56174, - 1.48659, - 1.41421, - 1.34535, - 1.28037, - 1.21942, - 1.16248, - 1.1094, - 1.06, - 1.01404, - 0.971286, - 0.931493, - 0.894427, - 0.859867, - 0.827606, - 0.797452, - 0.769231, - 0.742781, - 0.717958, - 0.694629, - 0.672673, - 0.651981, - 0.632456 < uke = ke + DiagonalMatrix @ udiag D ; eigsys = Transpose @ Sort @ Transpose @ Eigensystem @ uke DDDD ; eigsys @@ 1 DD 8 - 1.47947, - 0.677309, - 0.0120691, 0.874305, 2.01117, 3.40192, 5.03794, 6.91594, 9.03015, 11.3752, 13.9448, 16.7325, 19.7309, 22.9324, 26.3287, 29.9111, 33.6704, 37.5969, 41.6806, 45.9109, 50.277, 54.7677, 59.3715, 64.0765, 68.8706, 73.7416, 78.677, 83.664, 88.6899, 93.7417, 98.8066, 103.871, 108.923, 113.949, 118.936, 123.872, 128.743, 133.537, 138.242, 142.845, 147.336, 151.702, 155.933, 160.016, 163.943, 167.702, 171.284, 174.68, 177.882, 180.88, 183.668, 186.237, 188.582, 190.696, 192.572, 194.21, 195.589, 196.752, 197.529, 198.401, 198.521 < ListPlot @ eigsys @@ 2, 1 DDD 10 20 30 40 50 60 0.05 0.10 0.15 0.20 nvec = 2 * eigsys @@ 2, 1 DD ^2 8 0.000022207, 0.0000903391, 0.000208925, 0.000385613, 0.00063142, 0.000961112, 0.0013937, 0.00195303, 0.00266842, 0.0035753, 0.00471583, 0.00613926, 0.00790209, 0.0100676, 0.0127047, 0.0158857, 0.0196827, 0.0241618, 0.0293762, 0.0353558, 0.0420957, 0.0495424, 0.05758, 0.0660185, 0.0745868, 0.0829352, 0.0906501, 0.097285, 0.102405, 0.105643, 0.106752, 0.105643, 0.102405, 0.097285, 0.0906501, 0.0829352, 0.0745868, 0.0660185, 0.05758, 0.0495424, 0.0420957, 0.0353558, 0.0293762, 0.0241618, 0.0196827, 0.0158857, 0.0127047, 0.0100676, 0.00790209, 0.00613926, 0.00471583, 0.0035753, 0.00266842, 0.00195303, 0.0013937, 0.000961112, 0.00063142, 0.000385613, 0.000208925, 0.0000903391, 0.000022207 <
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ListPlot @ nvec D 10 20 30 40 50 60 0.02 0.04 0.06 0.08 0.10 Sum @ nvec @@ i DD , 8 i, 61 <D 2. uhvec
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This note was uploaded on 12/12/2011 for the course PHYS 238 taught by Professor Staff during the Fall '11 term at UC Irvine.

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Solution9.nb - Homework 9, Problem 2 ke = Table@ [email protected] j, 2,...

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