Showing Two Vectors are Eigenstates in a 2-Well System

“Show that

$$\begin{bmatrix} 1 \\ 1 \end{bmatrix} \text{ and } \begin{bmatrix} 1 \\ -1 \end{bmatrix}$$

are eigenvectors of the 2-well system Hamiltonian, and find the eigenvalues. ”

This SWBQ designs to be a small review for finding eigenvectors and eigenvalues, and also gives a glimpse into the general strategy for calculating the energies of eigenstates in the larger N-well system.

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