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Computing Outer Products
The Prompt
“Compute the outer product $\vert +\rangle \langle +\vert$”.
“Write down the projection operator for $\vert +\rangle_{x}$ in the z-basis in matrix and Bra-Ket notation. Then compute the outer product in the z-basis.”
Context
Oftentimes, students have been told that the outer product is a non-allowed matrix operation. Considering the outer product is essential for finding projection operators in quantum mechanical systems, these small white board questions are important for providing students practice in a new product. This is also a great activity for students to find the matrix representation of any bra-ket projection operators that have not yet been discovered.
This SWBQ sees possible inclusion in entry-level quantum mechanics lectures, particularly those that feature the varied ways to represent measurements mathematically.
