/sci/ - Science & Math

[Anonymous No.6243414]

What's up /sci/ is there a such thing as superposition of states? As in the unknown state of Schroedinger's Cat is two states in superposition

[Anonymous No.6243434]

bump

[Anonymous No.6243464]

The Schrödinger equation <span class="math">i\hbar\partial_t\Psi=\hat{H}\Psi[/spoiler] is linear, so if <span class="math">\Psi_1[/spoiler] and <span class="math">\Psi_2[/spoiler] are solutions, then so is <span class="math">\alpha_1\Psi_1+\alpha_2\Psi_2[/spoiler] for arbitrary complex <span class="math">\alpha_1[/spoiler] and <span class="math">\alpha_2[/spoiler], though in reality physical solutions are normalized, so given normalized solutions <span class="math">\Psi_1[/spoiler] and <span class="math">\Psi_2[/spoiler], <span class="math">\alpha_1\Psi_1+\alpha_2\Psi_2[/spoiler] is a normalized solution with <span class="math">\alpha_1[/spoiler] and <span class="math">\alpha_2[/spoiler] being complex numbers that satisfy <span class="math">\alpha_1^2+\alpha_2^2+[/spoiler]<span class="math">2\alpha_1\alpha_2\langle\Psi_1|\Psi_2\rangle=1[/spoiler]. Now say we are to observe a physical system, like Schrödinger's cat in a box. The observables are dead and alive. For each thing we can observe, there is some Hermitian operator <span class="math">\hat{Q}[/spoiler] whose eigenstates are observable states and whose eigenvalues are the numerical value of the observable (which I suppose would be either 1 for dead or 2 for alive or something like that). The eigenstates of a Hermitian operator are orthogonal (and since they're all normalized, orthonormal), so <span class="math">\rangle\Psi_1|\Psi_2\rangle=0[/spoiler], <span class="math">\alpha_1[/spoiler] and <span class="math">\alpha_2[/spoiler] satisfy <span class="math">\alpha_1^2+\alpha_2^2=1[/spoiler], and <span class="math">\alpha_1[/spoiler] and <span class="math">\alpha_2[/spoiler] are in fact the probabilities of measuring dead or alive respectively.

Shit nigger read a book.

[Anonymous No.6243475]

>>6243464

Working on it buddy, thanks for the response

[Anonymous No.6243542]

I wish that picture was larger and the text slightly clearer.

[Anonymous No.6243579]

>>6243464
This, and actually Schroedinger's Cat is a classical probability situation (combination of pure states (I think that's the right term)), it doesn't even demonstrate special features of quantum probability.