Particle in the box 

The following images shows a particle of mass m that is trapped in the second region of the potential shown that is from x=0 t x=L. In this same region the potential is zero. 

The particle in the box has solutions of the form: 

 (d) If we double the length of the box in the first image, so that the limits now go from  =  to  = +, what will be the wave function x() in this case ? (e) Derive an approximate expression for the uncertainty minimum at the moment for the extended box of question (d). Approximate what this value would be if the box measured 1 meter.

Vi = 0 = V = 0 V3 = 0 Regin 1 Regin 2 Region 3 I = 0 T =L 2 4x(x) = Vi sin(x). L