How do operators act on product kets like Sz|1>|0>?

[rubertoda]

If i have an operator (for example S^z) and then add it on two kets in a row

i e. S_z|1>|0>

How could you calculate this?

should i first add it on the |1> and then the |0> ?


help please

 

[TSny]

The answer would depend on how S_z is defined. S_z could be an operator that is defined to act only on the first ket in |1>|0>, so S_z|1>|0> = (S_z|1>)|0>. Or it could be defined to act only on the second ket.

Or, you could have a case where S_z = S_1z +S_2z where S_1z acts only on the first ket and S_2z acts only on the second ket. In that case S_z|1>|0> = (S_1z|1>)|0>+|1>(S_2z|0>)