How to write the map $\mathbb C\ni z\mapsto zv$ in bra-ket notation?

1

As part of a course, I've been asked to write a map $C\rightarrow H,z \rightarrow zv$ for $v \in H=C^3\otimes C^2$, $v=[1, 0, 0, 1, 0, 1]$ in bra-ket notation.

However, I never written such a map before, and must have missed the lecture. I would very much appreciate if someone show me some example of how to write this kind of thing.

humourous_mug

Posted 2019-02-26T13:57:24.847

Reputation: 19

you can find explanations of braket notation in here and links therein. Could you spell out what specifically (if anything) you find unclear in what is said there?

– glS – 2019-02-26T20:11:19.347

Answers

2

This map takes a complex number and returns a ket vector. In your case, this would simply mean writing $f(z) = z | v \rangle$.

Maybe a part of the exercise is to decipher $v$, then I would also expand it in ket notation: $| v \rangle = |0 \rangle \otimes |0 \rangle + |1\rangle \otimes |0 \rangle + |2\rangle \otimes |1 \rangle$.

It is somewhat tricky at first to think about vectors as maps from complex numbers to the vector space. If you want to describe a linear map $\mathbb{C} \rightarrow H$, then it's sufficient to specify $f(1)$, which is $v$.

Алексей Уваров

Posted 2019-02-26T13:57:24.847

Reputation: 398