Superposition Equation solution

[asechman]

Homework Statement

Hi everyone,
This is my first time posting, and I really need some help. I'm doing a project on Schrödinger's cat, concentrating on superposition and the linearity of operators.
I have this equation: |\psi\rangle = {3\over 5} i |A\rangle + {4\over 5} |B\rangle
but I don't know what amounts to plug in for A and B, as well as what amount the imaginary number represents, if anything.

Homework Equations

|\psi\rangle = {3\over 5} i |A\rangle + {4\over 5} |B\rangle

The Attempt at a Solution

I think I understand what the equation is saying, that if a particle can be at A and B, it can also be 3/5i in position A and 4/5 in position B. But beyond that, I don't know what step to take next.

Any input would be extremely helpful
thanks!

 

[Phlogistonian]

Hi asechman,
|A> and |B> are abstract representations of quantum states. You don't plug in anything for A and B. They are just labels used to distinguish the states.

Let's say you're making a measurement, and |A> and |B> represent two possible states resulting from that measurement. Then the formula

$$|\psi\rangle = N_A |A\rangle + N_B |B\rangle$$

means that the probability of finding the system in state A is

$$P_A = |N_A|^2 = {N_A}^*N_A$$

and the probability for finding the system in the other state is

$$P_B = |N_B|^2 = {N_B}^*N_B$$