For a particle with mass m confined to a 1 D box of length l with potential V(x)=0 inside the box and infinity outside it
Hello,
The problem can be approched by assuming the function as =Csin(kx) +Dsin(kx) and the constant can be obtained by substituting the above equation into equilibrium equation and satisfying for boundary conditions given in the problem. Here is the link for entire problem
https://www.google.co.in/url?sa=t&source=web&rct=j&url=http://home.iitk.ac.in/~madhavr/CHM102/Physical/Lec3.pdf&ved=2ahUKEwiJkYyR_p_fAhWFNY8KHTUNC1YQFjALegQIChAB&usg=AOvVaw2MaaprRBtFftv5cznH6rz_
Hope this helps....