Product State Bra Order: Correct Form?

[KFC]

In some books of quantum mechanics, the would like to write the product state as, for instance,

$$|\alpha\rangle_1|\beta\rangle_2$$

where 1 and 2 denotes different particle. If I want to write the corresponding bra vector, does the order matter? Which form is correct?

$${}_1\langle\alpha|{}_2\langle\beta|$$

or

$${}_2\langle\beta|{}_1\langle\alpha|$$

?

 

[Avodyne]

Since you labeled the states to show which applies to 1 and which to 2, the order doesn't matter. I think the more usual convention is to preserve the order, so that your first option would apply, but, again, as long as it's specified, it doesn't matter.

 

[Fredrik]

I'd choose the second option because it makes the "products" associative:

$$\Big({}_2\langle\beta|{}_1\langle\alpha|\Big) \Big(|\gamma\rangle_1|\delta\rangle_2\Big) ={}_2\langle\beta|\Big({}_1\langle\alpha|\gamma\rangle_1\Big)|\delta\rangle_2$$

But I agree that it doesn't really matter as long as you remember that the 1-bra acts on the 1-ket and so on.