I am puzzled by several questions of quantum mechanics.

First One:If I want to express a photon in the laevorotary state in
plane polarization representation, then how?
But I don't know what the two eigenstates are.
Second One: Don't use euqation but calculate the probability of a
harmonic oscillator staying at any position. The oscillation is
described as x = Asinwt.
Can anyone guset a formulation with an reasonable reason(can be not
very strict).

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