# Matrix element in problem with hydrogen atom

• I
Salmone
I have a problem in calculate a matrix element in a problem with hydrogen atom.

I have an hydrogen atom and Hamiltonian eigenstates ##|n,l,m>## where ##n## are energy quantum numbers, ##l## are ##L^2## quantum numbers and ##m## are ##L_z## quantum numbers, I have to calculate the matrix element ##<210|rsin(\theta)cos(\phi)|100>## with ##\theta \in [0,\pi]##, ##\phi \in [0,2\pi]##, ##r \in [0,+\infty]## and the result I get is ##\frac{4\pi}{27 \sqrt{2}}##, is it right?