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


```python
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
```


```python
display(H)
```


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



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


```python
eigvals
```




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




```python
eigvecs
```




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




```python

```

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notebooks/Untitled.ipynb
ZachGlassman/ZachGlassman.github.io
24791a01e6c567b1969b675f0dd6289f1b988853
Unlicense
notebooks/Untitled.ipynb
ZachGlassman/ZachGlassman.github.io
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Qwen/Qwen-72B
1. YES
2. YES