Consider a particle of mass m in an infinite spherical potential well of radius a For write down the energies and corresponding eigen functions ψ--(r,0.9). (3 pt) a) ne that at t-o the wave fu...
Consider a particle of mass m in an infinite spherical potential well of radius a For write down the energies and corresponding eigen functions ψ--(r,0.9). (3 pt) a) ne that at t-o the wave function is given by o)-A. Find the normalization constant A function in this basis. Solve for the coeffici You may find useful the integrals in the front of the (6 pt) d) Now consider the finite potential spherical well with V(r)- ing only the radial part of the eigenfunctions from part a) expand the initial wave ents c, in the expansion. exam. the front of the exam and assume that the energy is btain the solution for 1-0 and show that this solution fails when attempting to Return to the equation for u(r) listed in satisfy the boundary condition at r 0.
Consider a particle of mass m in an infinite spherical potential well of radius a For write down the energies and corresponding eigen functions ψ--(r,0.9). (3 pt) a) ne that at t-o the wave function is given by o)-A. Find the normalization constant A function in this basis. Solve for the coeffici You may find useful the integrals in the front of the (6 pt) d) Now consider the finite potential spherical well with V(r)- ing only the radial part of the eigenfunctions from part a) expand the initial wave ents c, in the expansion. exam. the front of the exam and assume that the energy is btain the solution for 1-0 and show that this solution fails when attempting to Return to the equation for u(r) listed in satisfy the boundary condition at r 0.