Matrix element in problem with hydrogen atom

In summary, the conversation discusses the calculation of a matrix element in a problem with a hydrogen atom. The matrix element in question is <210|rsin(\theta)cos(\phi)|100>, with specific ranges for theta, phi, and r. The result obtained is 4pi/27 sqrt(2). A link to the hydrogen wavefunctions is provided, and it is noted that psi_210 is independent of phi. A question is raised about the integral being zero due to this independence.
  • #1
101
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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?
 
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  • #3
Yes you are right, I must have gotten the angles mixed up and didn't realize it.
 

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