Quantum Fundamentals: NoTerm-2021
HW 1 : Due 2/10 Wed
- Ph425 Student Info
S0 4105S
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- What name would you like to use in class?
- What are your pronouns?
- What is a cool fact about you?
- Is there anything else you'd like me to know about you? (background that might be relevant, concerns about the course, how you've been personally impacted by COVID-19, struggles with motivation/depression, etc).
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- Circle Trigonometry
S0 4105S
On the following diagrams, mark both \(\theta\) and \(\sin\theta\) for \(\theta_1=\frac{5\pi}{6}\) and \(\theta_2=\frac{7\pi}{6}\). Write one to three sentences about how these two representations are related to each other. (For example, see: this PHET)
- Matrix Refresher
S0 4105S
Calculate the following quantities for the matrices:
\[A\doteq
\begin{pmatrix}
1&0&0\\ 0&0&1\\ 0&-1&0\\
\end{pmatrix}
\hspace{2em}
B\doteq
\begin{pmatrix}
a&b&c\\ d&e&f\\ g&h&j\\
\end{pmatrix}
\hspace{2em}
C\doteq
\begin{pmatrix}
\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\\
\end{pmatrix}
\]
and the vector:
\[\left|D\right\rangle\doteq
\begin{pmatrix}
1\\ i\\ -1\\
\end{pmatrix}
\hspace{2em}
\]
- \(AB\)
- \({\rm tr} (B)\)
- \(A\vert D\rangle\)
- \(\det(\lambda{\cal I}-A)\) where \(\lambda\) is a scalar.
- \(C^{-1}\) (Hint: Geometrically, what is the \(C\) transformation? What transformation undoes what \(C\) does?)
- Complex Arithmetic: Rectangular Form
S0 4105S
For the complex numbers \(z_1=3-4i\) and \(z_2=7+2i\), compute:
- \(z_1-z_2\)
- \(z_1 \, z_2\)
- \(\frac{z_1}{z_2}\)