(Solved): Question 2: The Time-Independent Schrodinger Equation in Spherical Coordinates (a) Consider the wa ...

Question 2: The Time-Independent Schrodinger Equation in Spherical Coordinates (a) Consider the wavefunction \( \psi(r, \theta, \phi)=A e^{-r / a} \), where \( A \) and \( a \) are constants. Find \( E \) and \( V(r) \) assuming that \( V(r) \rightarrow 0 \) as \( r \rightarrow \infty \). (b) Consider the wavefunction \( \psi(r, \theta, \phi)=A e^{-r^{2} / a^{2}} \), where \( A \) and \( a \) are constants. Find \( E \) and \( V(r) \) assuming that \( V(0)=0 \).