Question 6 (Spherical symmetric potential) In quantum mechanics we know that when a spherical symmetric potential V(x,y,z) = V(r) acts on a particle is angular momentum operator L² commutes with the Hamiltonian ħ² 1 ə p² H=+V(r) = 2m a -2²0) + + V (r) L² 2mr² 2m r² 2 dr. (1². Note that since the angular dependence is found only in the L², we can separate variables in the wave function. Consider a particle in a spherical and infinite potential well: V(r) = {0 for 0≤rsa loo for r>a a) Write the differential equation of the radial part. b) Compute the energy levels and the stationary wave function for l = 0 (Use change of variable such that U(r)=rR(r)).

Question 6 (Spherical symmetric potential) In quantum mechanics we know that when a spherical symmetric potential V(x,y,z) = V(r) acts on a particle is angular momentum operator L² commutes with the Hamiltonian ħ² 1 ə p² H=+V(r) = 2m a -2²0) + + V (r) L² 2mr² 2m r² 2 dr. (1². Note that since the angular dependence is found only in the L², we can separate variables in the wave function. Consider a particle in a spherical and infinite potential well: V(r) = {0 for 0≤rsa loo for r>a a) Write the differential equation of the radial part. b) Compute the energy levels and the stationary wave function for l = 0 (Use change of variable such that U(r)=rR(r)).