The electron in a hydrogen atom is in the state |v) N[3]w100) + 4 |w211)] where ynlm represents the spatial eigen functions of hydrogen atom. (a) Find N such that the above state normalized. Assume N is real and positive. (b) Is y) an eigen state of the Hamiltonian of hydrogen atom? Justify your answer. (c) Determine expectation value of the Hamiltonian in terms of eigen energies Ei and E2.

The electron in a hydrogen atom is in the state |v) N[3]w100) + 4 |w211)] where ynlm represents the spatial eigen functions of hydrogen atom. (a) Find N such that the above state normalized. Assume N is real and positive. (b) Is y) an eigen state of the Hamiltonian of hydrogen atom? Justify your answer. (c) Determine expectation value of the Hamiltonian in terms of eigen energies Ei and E2.