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Showing Two Vectors are Eigenstates in a 2-Well System

Prompt

“Show that $\left[\begin{array}{c} 1\\ 1\\ \end{array}\right]$and$\left[\begin{array}{c} 1\\ -1\\ \end{array}\right]$ are eigenvectors of the 2-well system Hamiltonian, and find the eigenvalues.”

Context

This SWBQ is designed to be a small review for finding eigenvectors and eigenvalues, and this activity also gives a glimpse into the general strategy for calculating the energies of eigenstates in the larger N-well system. The 2-well system is one of the simplest cases students can analyze using the matrix form Hamiltonian.

Wrap Up


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