An electron in a one-dimensional infinite square well potential of length L is in a
quantum superposition given by ψ = aψ1+bψ2, where ψ1 corresponds to the n = 1 state, ψ2 corresponds to the n = 2 state, and a and b are constants. (a) If a = 1/3, use the
normalization requirement for ψ to determine the value of b. (b) If we perform a
measurement of the energy of the electron, what is the probability we will measure E1?
What is the probability we will measure E2?
The Attempt at a Solution
So basically I have to find the ψ of an electron in the ground state and then in the n = 2 state? Do I solve for that? And how do I normalize a wave function that doesn't have "i" in the exponent? I've only learned that normalizing is making the "i" a "-i" as the conjugate, and then multiplying it with the original function. How do I normalize something without "i" in its exponent?