Beam splitter->ONB->transition amplitudes

1. Jun 20, 2011

klabautermann

1. The problem statement, all variables and given/known data
a general beam splitter is charcatericed by its transition amplitudes Sxy=<Xin|Yout> where X,Y=L or R. |Lin> represents a photon wich leaves the beam splitter to the right. we are only considering photons with the same energy and polarization and neglect all other state parameters.
the beam splitter is loss-free, what mathematical properties has the matrix S of transition amplitudes?

2. Relevant equations

3. The attempt at a solution
{|Xin>,|Yout>} form an orthonormal basis and |Yout>=$\sum$SXY|Xin>. S describes the change of basis. S preserves the inner product, therefor S is unitary.

i am reviewing problem sets, because i have quantum mechanics exam tomorrow. i have a question. could i also take for example |Yin>, |Xin> as basis vectors? why do i know that S preserves the inner product.

thanks!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution