The state of a system, indeed any system, whether that be described as being tangible ''outside'' or even the construction of the incorporeal inside, that of subjective experience should be described by a state vector, given as $$|\Psi>$$. The state of a vector is the overall description of the possibilities that may arise when a collapse of the wave function has appeared. The collapse of the wave function happens upon a measurement. Observable's are resultant from measurements. Observables in the language of quantum mechanics are Hermitian Matrices which means it will produce a real number.
The definition, in totally mathematical terms right now, is given by the following.
$$<a| M^{\dagger}|b>^{*}$$
where the <a| is acting like a complex conjugate, in fact, this has been complex conjugated where all rows and columns have been interchanged. Incidently, M on <a| will give you a vector, but M and <a| after this onto |b> will give you a number. It won't give you a vector in this case, it's just a number.
So you get from $$<b|M|a>$$ to the expression $$<a| M^{\dagger}|b>^{*}$$ by complex conjugating it. In fact, if it is Hermitian you can now state it as
$$<b|M|a> = <a| M|b>^{*}$$
where we have just erased the conjugation dagger sign. This just means it is equal to it's Hermitian conjugate. This is the true definition of the meaning of Hermitian.
Now the wave function, the ''configuration'' of states of a system describes all possible solutions which may or may not occur for a system. A photon bouncing of a mirror does not take one path alone, in fact, will take every angle possible to account for the wave function which smears every possibility over a given region. Given a large enough region, you may even call it infinite.
And now, given all this information, I ask, what is a set of possibilities, if not the analog of such a wave function? In fact, as history goes, when phsyicists realized that a wave function existed, they believed it was a product of the mind, simply, just a way for us to catalogue the events. This subjective idea of the wave function soon diminished and we realized atleast in principle, there was something physical behind this [1]. However, if we take the basic idea of the wave function seriously, then it should not be bound to physical objects alone. That even subjective experiences may be subject to such a phenomenon as well.
Suppose that every experience is ruled by a wave of possibilities, given as $$\Psi$$. This description will state that before anything has been resolved by the action of a human being, or maybe even by thought, the wave function itself will be spread among many different possibilities.
The probability of finding any one of those experiences, or thoughts or actions result in a collapse of the wave function, traditionally given by the probability postulate as
$$\mathbf{Tr} \rho = \mathcal{1}$$
The density matrix here, in case anyone jumps down my throat, is given by the unit matric which will give a Hermitian Operator, which is by definition as we have covered, an observable. The trace is simply the sum over all possible Eigenstates given as $$\lambda_i$$ where $$i = (1,2...n)$$.
In quantum mechanics, rather than applying matrix mechanics, we will find the probability of a system to be
$$\int_{\Omega} |\psi|^2$$
Where $$\Omega$$ is our boundary [2].
The real crux of this arguement, is that consciousness, the acts of consciousness or/and the conscious acts of decisions are subject to collapses of the wave function. You could have the choice of turning two playing cards over that have been placed in front of you. Those cards will be represented by a wave function:
$$|\Psi> = \frac{1}{2}i|A> + \frac{1}{2}|B>$$
This will, not in a physical sense, but a subjective sense describe the possibilities that may arise from either state which depend on their orientation to each state in the complex plane. Upon measurement, of either playing card in the subjective subliminal sense will yeild the value upon the measurement of either card to account for the collapse of the wave function postulate.
So, it can easily be shown that somehow probabilities and the wave function generally describe the actions of choice and will have perhaps massive implications to the philosophical arguements between, determinism vs indeterminism.
[1] - I provided evidence recently that the wave function was physical when pressed by alphanumeric.
[2] - In dirac notation $$<\psi_n|\psi_m> = 0$$ unless psi_m and psi_n correspond to the same eigenvectors.
