Can Photon States Be Represented as Column Vectors in Quantum Mechanics?

[suma]

I have few questions to ask:

1. Can a photon state be written as
|ψ> = [cos(θ) sin(θ) exp(i*ø)] in column vector form

2. When a general photon state|ψ> = [cos(θ) sin(θ) exp(i*ø)] passes through a linear polarizer [1 0; 0 0] we get [cos(θ) 0] at the output but not [1 0] as is usually found in textbook

thanks

 

[Simon Bridge]

Presumably you mean to describe only the polarization state of the photon.
You should realize that x and y directions are meaningless without a polarizer.
You appear to be trying to resolve the classical and quantum descriptions of polarization - this should be done via the correspondence principle.

See:
http://mathpages.com/rr/s9-04/9-04.htm
... you need to scroll right down to the bottom to get to the QM version of linear and circularly polarized light.