by the 17. Calculate the average linear momentum of a particle described following wavefunctions: (a) cos(kx), (b)e-², where in each one r goes from -∞ to +∞.

16. Consider the wave function Mx) = (alT)" exp(-ax12) Calculate (x) for n = 1, 2. Can you quickly write down the result for (")?

4. Normalize the following wavefunctions 4 55 (a) v(x) = sin (#2); =sin(); for a particle in a 1D box of length L. (b) (2) = xe-z|2 (c) (x) = e(x²/a²)+(ikz) 5. In a region of space, a particle with mass m and with zero energy has a time- independent wave-function (x) = Ae-2/12, where A and L are constants. Use your knowledge of the Schrödinger equation to determine the potential energy V(x) of the particle. Plot the potential function? What is the minimum potential energy for the particle, if it is an electron and L = 1 fm? Is this potential repulsive or attractive?