Are Stern-Gerlach Filters Modeled by Hermitian Operators in Quantum Mechanics?

[Ray]

Can anyone help me with this simple question based on Feynman's Vol 3? Suppose I have a sequence of filters designed to show the suprising result that extra filters allow previously blocked photons, polarised light, spin one and spin one half particles etc. to get through. Then matrix multiplication models the sequential measurements, BUT ARE THE FILTERS THEMSELVES MODELLED BY HERMITIAN OPERATORS IN MATRIX FORM? As far as I can tell Feynman deals with a change of basis matrix which is orthogonal and not Hermitian. I have only a rudimentary knowledge of QM so the question isn't meant to be difficult, I just want to know if a filter rotated through an angle is a Hermitian operator and if it is what is its base dependent form.

 

[azntoon]

Thanks A:The answer to your question is no. A filter is not a Hermitian operator in the quantum mechanical sense. A Hermitian operator is an operator which is equal to its own adjoint (the complex conjugate of the transpose). Filters are typically just pieces of polarising material that lets through certain polarisations and blocks others. They can be thought of as an operator which acts on a state vector, but they are not Hermitian operators.