Re: I am puzzled by several questions of quantum mechanics.

dijkstra wrote:

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.

Momentum eigenstates are plane waves, and they can be polarized in one direction or the other. So far it's no different than the classical field. But the quantum field follows deBroglie's relation, so the momentum of the field goes in steps of h/lambda. The occupation number formalism is usually used to track the number of steps that are in each wavelength.

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).


Easy: zero. By the uncertainty principle, as the position is confined to a smaller region, the momentum gets larger and it's not going to stay where you put it.

To be a little fancier, like supposing the position has a Gaussian distribution with width w about point x, and then asking how the probability distribution evolves over time, you need to solve Schroedinger's equation.
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