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)