What does the notation $|\psi(0)\rangle = |0\rangle|n=0\rangle$ mean?

Question

Please, help me understand that, if on RHS we have a matrix product of two column vectors?

Rammus · Accepted Answer · 2020-11-05 15:56:21Z

2

This is common shorthand for the tensor product. That is, you should read it as $|0 \rangle \otimes | n=0\rangle$.

answered Nov 5, 2020 at 15:56

Rammus

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$\begingroup$ |a⟩⊗|b⟩=|a,b⟩ |a⟩⊗|b⟩=|ab⟩ , Are these two notations also true? $\endgroup$
– Binshumesh sachan
Commented Nov 5, 2020 at 16:06
$\begingroup$ They're also notations I've seen elsewhere, yeah. $\endgroup$
– Rammus
Commented Nov 5, 2020 at 16:07
$\begingroup$ I would doubt it. What kind of matrix product are you thinking of? If written $|a \rangle \langle b|$ then it denotes the outer product usually but this would not make sense given the LHS of your equation which is a vector $|\psi(0)\rangle$. The only other possibility I could imagine (but which I very very much doubt is the case) is that it denotes an elementwise product but this only makes sense if $|\psi(0)\rangle$, $|0\rangle$ and $|n=0\rangle$ are all vectors from the same dimensional vector space. If this notation is not specified explicitly then I am confident it is the tensor product. $\endgroup$
– Rammus
Commented Nov 5, 2020 at 16:14
$\begingroup$ I just checked the reference of the book which I am reading. It denotes the tensor product. Thanks for your help. These different notations made me confuse. $\endgroup$
– Binshumesh sachan
Commented Nov 5, 2020 at 16:17

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