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 Schrodinger'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

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

 

[Moetasim]

I can provide some insight into the superposition equation and how it relates to Schrodinger's cat. The equation you have provided is known as a wave function, which represents the quantum state of a particle. In this case, the particle is in a state of superposition, meaning it exists in multiple states simultaneously.

The i in the equation represents the imaginary unit, which is used in quantum mechanics to represent the phase of the wave function. This phase has physical significance and can affect the behavior of the particle.

As for the values of A and B, they represent the different possible states of the particle. In the case of Schrodinger's cat, A could represent the cat being alive and B could represent the cat being dead. The equation is saying that the particle (in this case, the cat) can exist in both states at the same time, with a probability of 3/5 for being in state A and 4/5 for being in state B.

To fully understand the implications of this equation, you may need to delve deeper into the principles of quantum mechanics and the concept of superposition. I suggest consulting with your instructor or conducting further research to gain a better understanding of this equation and its significance in the context of Schrodinger's cat.