1. The problem statement, all variables and given/known data Hello. Imagine a particle bound in a square well potential of potential energy V0 if |x| > a 0 if |x| < a The wave function of the particle is: (ignoring the time dependency) -A*exp(kx) if x<-a B*sin(3*pi*x/4a) if |x|<a A*exp(-kx) if x>a where k = sqrt(2mE)/ħ Find the energy of the particle. 2. Relevant equations 3. The attempt at a solution First of all I determined the value of A through the condition of continuity at the boundaries: A*exp(-k*a) = B*sin(3*pi*a/4a) A*exp(-k*a) = B/sqrt(2) A = B*exp(ka)/sqrt(2) Rewriting the wave function: -B*exp(k[x+a])/sqrt(2) if x<-a B*sin(3*pi*x/4a) if |x|<a B*exp(-k[x-a])/sqrt(2) if x>a After that I decided to use the normalization condition to find the value of k. [itex]\int[/itex]dx <ψ|ψ> = 1 Separating the integral into three, one for each region, I concluded that: ∫dx A2 exp(2kx) = B2/4k ∫dx A2 exp(-2kx) = B2/4k ∫dx A2 sin2(3*pi*x/4a) = B2(a+1/2a) Therefore: B2/2k + B2(a+1/2a) = 1 B2(1/2k + a + 1/2a) = 1 However this doesn't help me much... I don't know what I should do next, or if what I'm doing is getting me closer to the answer.. The correct answer is: E = (9/32) π2ħ2/ma2 Thanks for taking the time to read my problem.