Bra of product state

1. Dec 15, 2008

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

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

???

2. Dec 15, 2008

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.

3. Dec 16, 2008

Fredrik

Staff Emeritus
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.