In [7]:

    

from sympy import *
init_printing(use_latex='mathjax')
from IPython.display import display


    

In [33]:

    

delta = Symbol("Delta")
x = Symbol("x")
y = Symbol("y")
V = Symbol("V")
H0 = Matrix([[-delta/2,0],[0,delta/2]])
V = Matrix([[0,V],[V,0]])
H = H0 + V


    

In [26]:

    

display(H)


    

    






$$\left[\begin{matrix}- \frac{\Delta}{2} & V\\V & \frac{\Delta}{2}\end{matrix}\right]$$

In [27]:

    

evecs = H.eigenvects()
eigvals = [evecs[0][0],evecs[1][0]]
eigvecs = [evecs[0][2],evecs[1][2]]


    

In [28]:

    

eigvals


    

    
Out[28]:





$$\left [ - \frac{1}{2} \sqrt{\Delta^{2} + 4 V^{2}}, \quad \frac{1}{2} \sqrt{\Delta^{2} + 4 V^{2}}\right ]$$

In [29]:

    

eigvecs


    

    
Out[29]:





$$\left [ \left [ \left[\begin{matrix}- \frac{V}{- \frac{\Delta}{2} + \frac{1}{2} \sqrt{\Delta^{2} + 4 V^{2}}}\\1\end{matrix}\right]\right ], \quad \left [ \left[\begin{matrix}- \frac{V}{- \frac{\Delta}{2} - \frac{1}{2} \sqrt{\Delta^{2} + 4 V^{2}}}\\1\end{matrix}\right]\right ]\right ]$$

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