1a. Show that the B cos(ax) is a solution for the the Schrodinger equation for a particle in a box that is centered around the x axis and goes from x=-L/2 to +L/2.

1b. From the boundry conditions show a=np/L. n= odd numbers

1c. Show that the eigenfunctions are orthogonal by showing that the intergal of Y₁Y₃ over all space is 0.

2. What is the second derivative of Bxe^-ax with respect to x?

3. What are the values of each of the following assuming y is nice wave function for a system,.

a) integral of y²dt over all space =

b) integral of y_iy_jdt over all space = {i not equal j}

c)integral of y_iHy_jdt over all space = {H is Hamiltonian or the system. Do this for both i equal j and i not equal j and you should show the answer in two steps}

4. text 9.44

5. In the Schrodinger equation, HY = EY, the square of the wave function, Y², is interpreted as

a) the energy of the system

b) the momentum of the system

c) the probability of finding the system at some particular configuration.

d) the square of the momentum.

6. Quantum mechanical equations frequently involve the quantity, 2mE. This quantity is

a) the momentum squared b) the kinetic energy c) the Plank frequency d) the uncertainty divided by h