User:Superdan006/Sandbox/thesis

Hamiltonian Matrix for the Double Well Potential, N=4

${\begin{bmatrix}16&-4C&0&0&0\\-4C&10&-2C{\sqrt {6}}&0&0\\0&-2C{\sqrt {6}}&8&-2C{\sqrt {6}}&0\\0&0&-2C{\sqrt {6}}&10&-4C\\0&0&0&-4C&16\end{bmatrix}}$

$C={\frac {E_{j}}{E_{c}}}$

Input matrix for C = 1 (http://www.bluebit.gr/matrix-calculator/):

16.000000 -4.000000  0.000000  0.000000  0.000000
-4.000000 10.000000 -4.898979  0.000000  0.000000
 0.000000 -4.898979  8.000000 -4.898979  0.000000
 0.000000  0.000000 -4.898979 10.000000 -4.000000
 0.000000  0.000000  0.000000 -4.000000 16.000000

Eigenvalues:

( 1.505393, 0.000000i)
( 8.000000, 0.000000i)
(13.265353, 0.000000i)
(19.229254, 0.000000i)
(18.000000, 0.000000i)

Eigenvectors:

( 0.131140, 0.000000i) (-0.316228, 0.000000i) ( 0.468641, 0.000000i) (-0.513009, 0.000000i) (-0.632456, 0.000000i)
( 0.475207, 0.000000i) (-0.632456, 0.000000i) ( 0.320392, 0.000000i) ( 0.414159, 0.000000i) ( 0.316228, 0.000000i)
( 0.716911, 0.000000i) ( 0.000000, 0.000000i) (-0.596196, 0.000000i) (-0.361370, 0.000000i) ( 0.000000, 0.000000i)
( 0.475207, 0.000000i) ( 0.632456, 0.000000i) ( 0.320392, 0.000000i) ( 0.414159, 0.000000i) (-0.316228, 0.000000i)
( 0.131140, 0.000000i) ( 0.316228, 0.000000i) ( 0.468641, 0.000000i) (-0.513009, 0.000000i) ( 0.632456, 0.000000i)