I1

3. Consider the potential ha2 1 V(r) = m cosh ar (a) find the energy and wave function of ground state of this potential. (Hint: Using the fact that tanh I' = 20shi z (b) Show that the function k(r) = A(ik atanh(ar) jerks is the solution of Schrodinger equation for any positive energy. Find the asymptotic form of wk and find the R and T of this system. You should find that any particle can go through this potential with reflection-less property