Frequently-asked questions, and typo, lectures 46 – 48

Frequently-asked questions

Does a pure state have to be an equal linear superposition of states? Is it still a pure state if the coefficients of the states differ?

A pure state does not have to be an equal linear superposition of basis states. It can be any linear superposition of basis states (including just being in a basis state).

What does “definite parity” mean?

Either even parity or odd parity, but not some mixture (which would actually not have any parity at all).

Typographical errors

In Video 46a, starting at 5:57 (slide 6), there is a typographical error in the expression at the end of the second last line of the slide. Instead of \(\left\langle 0 \right|{\hat a_\lambda }{\hat b_j}\hat a_j^+ \hat b_\lambda ^+ \left| 0 \right\rangle \), we should have \(\left\langle 0 \right|{\hat a_\lambda }{\hat b_j}\hat b_j^+ \hat a_\lambda ^+ \left| 0 \right\rangle \) (the “a” and “b” have been transposed at the end of the expression). This is corrected in the slides, but is not corrected in the video.