Dear all, sorry I made a new post similar to the previous post "Initial conditions..", however, a critical point was missed in the previous discussion: The initial conditions y(0)=1 and y'(0)=0 are fine and help in solving the Schrödinger equation, however, studying free electrons, the equation cannot be solved neither for the particle in the box , or for a finite linear motion harmonic oscillator as far as I can see from the literature. When I solve the eqn, HY=EY , I can set E= p/2m or E= ground state energy. In either cases, I get a result where some unknown constant appears. This constant can be solved using the Born Sommerfeld condition, but because the solution is not square integrable, it gives complex values. How can I solve the unknown constant for a solution of the Schrödinger eqn. where the above given initial conditions are used? Thanks!