Solution9.nb

# Solution9.nb - Homework 9, Problem 2 ke = Table@ [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */ j, 2,...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 <
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 8

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online