{{page>wiki:headers:hheader}}

%% Instructions:
%% 1. Replace "The Question" with the question.
%% 2. Change qmswzzz everywhere (2x) to the basename of this file.
%% 3. Upload the PDF and PPT versions of the question.
%%    (Make sure to use the same basename.)
%% 4. Change xx in the 2-letter acronym in the course footer to reference
%%    the correct course.
%% 5. Delete these instructions when done!


====== Properties of Outer Products ======


===== The Prompt =====

**Compute the outer product of the general state vector**

$$
\vert \psi\rangle=\left[\begin{array}{c}
\sin(\frac{\theta}{2})\\
\cos(\frac{\theta}{2})e^{i\phi}\\ \end{array}\right]
$$

**Take the determinant of the computed 2 x 2 matrix.**


===== Context =====

After being introduced to the density matrix, students are commonly skeptical about how useful it can be in finding probabilities and describing mixed states. This [[strategy:smallwhiteboard:|SWBQ]] introduces several of the properties of the density matrix and helps students transition into making states described by density matrices. The activity also shows that for any density matrix formed by the outer product of a general state vector with itself must have $\text{Tr}(\vert \psi\rangle \langle\psi\vert) = 1$ and $\text{Det}(\vert \psi\rangle \langle\psi\vert) = 0$. 



===== Wrap Up =====

FIXME - Extra Information "After being introduced to the density matrix, students are commonly skeptical about how useful it can be in finding probabilities and describing mixed states."

{{swbq:spsw:spswdensopprop.ppt|Powerpoint slide}}
\\\\
{{swbq:spsw:spswdensopprop.pdf|PDF slide}}



{{page>wiki:footers:courses:spfooter}}

{{page>wiki:footers:topics:qmfooter}}