The wave function of a particle in two dimensions in plane polar coordinates is given by: T Y(r,0) = A.r.sinoexp 2a0. where A and ao are positive real constants. 1. Find the constant A using the normalization condition in the form SIY(r.0)|²rdrd0 = 1 2. Calculate the expectation values of r, and ². 3. Assuming that the momentum operator in plane polar coordinate is giving in the form p=calculate the expectation values of p and p². 4. Find the standard deviations of r and p and show that their product is consistent with the Heisenberg uncertainty principle.

The wave function of a particle in two dimensions in plane polar coordinates is given by: T Y(r,0) = A.r.sinoexp 2a0. where A and ao are positive real constants. 1. Find the constant A using the normalization condition in the form SIY(r.0)|²rdrd0 = 1 2. Calculate the expectation values of r, and ². 3. Assuming that the momentum operator in plane polar coordinate is giving in the form p=calculate the expectation values of p and p². 4. Find the standard deviations of r and p and show that their product is consistent with the Heisenberg uncertainty principle.