1. A particle is represented by the following wave function: y(x)=0 x≤-L/2 = C(2x/L+1) -L/2<x<0 = C(-2x/L+1) 0 < x <+1/2 +L =0 x>+L/2 (a) Use the normalization condition to find C. (b) Evaluate the probability to find the particle in an interval of width 0.010L at x = L/4 (that is, between x 0.245L and x = 0.255L. No integral calculation is necessary for this calculation.) = (c) Evaluate the probability to find the particle between x 0 and x = +L/4. (d) Find the average value of x and rms of x: x = √ (x²) avg 2. Show that the average value of x² in the one-dimensional infinite potential energy well is L²(1/3-1/2n²²) 3. Use the result above to show that, for the infinite potential energy well, defining Ax √(x²) -(x)² gives Ax L√1/12-1/2π²n²