1. The problem statement, all variables and given/known data I am trying to calculate the charge density in the first subband (n=1) of the quantum well of length L as shown in the below figure. here is the electron wave function for the first sub-band and its value (from relevant equation 1) is given as Ψ12(x) = 2/L*sin2(πx/L) from Schrodinger equation total electron charge density is given by n(x) = N1×Ψ12(x) where N1 is the electron charge density in the first subband(n=1). hence for charge density at x = L/2 the above equation becomes n(L/2) = N1×Ψ12(L/2) = N1×2/L*sin2(π/2) --result 1 But from wave function normalization,that is the probability of finding electron between 0 and L is one(from relevant equation 2) Ψ12(L/2) ≈1, then the total electron charge density at x=L/2 is n(L/2) = N1×1 --result 2 2. Relevant equations wave-function for the electrons in the quantum well sub bands wave function normalization(that is the probability of finding electron between 0 and L is one) 3. The attempt at a solution When i made attempts for the solutions i got two results result 1 and result 2 as above. Now my question is which is the correct result from these two..?