(Solved): Superposition states of hydrogen atom. Suppose the hydrogen atom is in a quantum superposition ...

Superposition states of hydrogen atom. Suppose the hydrogen atom is in a quantum superposition state described by the following three different eigenfunctions ${\psi }_{n,l,m_l}$ : $\Psi ={\left(\frac{3}{8}\right)}^{1/2}{\psi }_{2,1,1}+{\left(\frac{3}{8}\right)}^{1/2}{\psi }_{2,1,0}+A{\psi }_{2,1,-1}$ - Normalize the function, e.g find the value for $A$ that ensures normalization of the $\Psi$ - If we measure the values of Energy, angular momentum, and its projection, what values will we obtain and with what probabilities? - Compute the average energy, angular momentum, and its projection. - Write down the time-dependent wave function $\Psi (t)$ - Will the average value $⟨r⟩$ change over time?