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Hi,
I'm doing a homework problem in my modern physics class and I'm stuck at a point. The question is "Show that the radial probability density of the 1s level in hydrogen has
its maximum value at r = a0, where a0 is the Bohr radius"

I know that the radial schrodinger equation will give me the part of the answer that I need. I know that ψ(r,θ,phi) is found by separation of variables and that once I find ψ I can find the probability at any r by using

P(r)dr = abs(ψ)^2dV = (abs(ψ)^2)*4∏(r^2)dr

I know what my r is. My problem is solving the radial schrodinger equation. I have no idea what to do. The book gives boundary conditions: lim(R(r)) r-->∞ = 0 and the angular components must be periodic (f(θ) = f(θ+2∏n))