Electron in two Potential Wells

1. The problem statement, all variables and given/known data



An electron can be in one of two potential wells that are so close that it can “tunnel” from one to the other (see §5.2 for a description of quantum- mechanical tunnelling). Its state vector can be written

|ψ⟩ = a|A⟩ + b|B⟩, (1.45)

where |A⟩ is the state of being in the first well and |B⟩ is the state of being in the second well and all kets are correctly normalised. What is the probability of finding the particle in the first well given that: (a) a = i/2; (b) b = e^(i*pi); (c) b = 1/3 + i/√2?



2. Relevant equations



a*a is the probability of finding a particle in state A



3. The attempt at a solution



The question is confusing me. I don't know what the second b is for. Also, these are supposed to be normalized according to the question, but b*b (for the first b) would be 1 all by itself. Is this question ok, and I am just missing something?



Thanks,

Chris Maness

1. The problem statement, all variables and given/known data







2. Relevant equations







3. The attempt at a solution