Question

If anyone is familiar with Dirac notation, would you be willing to check this for me?

Answer 1

I'm trying to explain superposition of the Schrodinger Cat paradox in Dirac notation, but I'm not sure if this is correct?

We put a cat in a box, and in this box we have a measurement device (such as a Geiger counter), a small amount of radioactive material and a vial of poison (it is set up such that direct interference with the cat is impossible). Over the period of one hour, there is a fifty-fifty chance that the radioactive material decays; if it does so, the Geiger counter recognises this and subsequently releases a hammer, breaking the vial of poison and killing the cat. It is also equally likely that the material does not decay. Until we physically open the box and observe the cat, the wave function suggests that the cat is in a superposition state of both being alive and dead simultaneously, and it is only when we open the box that the wave function collapses, and reduces to a single state, of being alive or dead:

Initial state (putting the alive cat in the box): \[|up >⊗|ready >⊗|alive > \]
During the period of one hour: \[\frac{ 1 }{ \sqrt{2} } |up > ⊗|alive> +\frac{ 1 }{ \sqrt{2} } |down> ⊗|dead>\]
Moment of measurement/observation: \[|up > ⊗|alive> \text{OR} \quad |down> ⊗|dead>\]
With the probability of either occurring equal to \[\bigg(\frac{ 1 }{ \sqrt{2} } \bigg)^{2}\]

Answer 2

I'm really not familiar with Dirac notation, I've seen this exact thing computed before, and it definitely makes sense what answer you've arrived at, since there should be a 1/2 chance of either happening since the cat is either alive or dead the total probabilities add up to 1, which is 100%.

Answer 3

okay as long as it makes sense that's okay! Thank you! :-)