Explain why the wave function must be finite, unambiguous, and continuous.

Show that the following wave function is normalized. Remember to square it first. Limits of integration go from -infinity to infinity. DO NOT SKIP ANY STEPS IN THE PROCEDURE

Consider a particle of mass m which can move freely along the x axis anywhere from x=-a/2 to x=a/2, but which is strictly prohibited from being found outside this region (technically this is the infinite square well potential). 1. Verify that the attached wavefunction is a solution of the Schrodinger's equation. Consider V=0.  2. Deduce the value of the energy E. 3. Verify the  uncertainty principle

Please don't provide handwritten solution .....    Determine the normalization constant for the wavefunction for a 3-dimensional box (3 separate infinite 1-dimensional wells) of lengths a (x direction), b (y direction), and c (z direction).