Please handwrite it or type in readable format (don't copy chatgpt answer)

(A) (4 points) Write down a normalized superposition (linear combination) wavefunction for the Hydrogen atom in which an electronic state has twice as much contribution from (n=1,1=0) as from (n=2,l=1,m=1). Write both the ket and wavefunction forms. Is this superposition an eigenstate of the Hydrogen atom Hamiltonian? (B) (4 points) Prove that the expectation value of r in the 1s and 2s states for a hydrogen atom is 23a0 and 6a0, respectively. (C) (3 points) Prove that the expectation value of the potential energy is equal to twice the expectation value of the total energy V>=2 for a 2pz electron. The 2pz orbital is not an eigenfunction of V, so you'll need calculus to solve for V. The equation for V is given in McQuarrie and the notes