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Hi guys I'm having a problem with calculations involving the ground state of the hydrogen atom. My main issue comes from the wavefunction of this state: i.e.

[tex] \Psi(r) = \frac{1}{\sqrt{\pi a^3}}\exp{\frac{-r}{a} [/tex]

My main problem seems to come from the fact that this function has no complex element (no i). Which is odd since I thought the wavefunction HAD to be complex also it means there is no complex conjugate. This causes a problem in my calculations for expectation values and probability integrals because there is still a pesky exponential term I can't get rid of which throws a spanner into my working?

One calculation it agravated was finding the probability of the electron being in a classically forbidden zone (i.e with r < a -the Bohr radius)

[tex] \int_0^a{\Psi(r)^2}dr [/tex]

Anyone got any tips, is it my definitions of should I look closer at my algebra?

[tex] \Psi(r) = \frac{1}{\sqrt{\pi a^3}}\exp{\frac{-r}{a} [/tex]

My main problem seems to come from the fact that this function has no complex element (no i). Which is odd since I thought the wavefunction HAD to be complex also it means there is no complex conjugate. This causes a problem in my calculations for expectation values and probability integrals because there is still a pesky exponential term I can't get rid of which throws a spanner into my working?

One calculation it agravated was finding the probability of the electron being in a classically forbidden zone (i.e with r < a -the Bohr radius)

[tex] \int_0^a{\Psi(r)^2}dr [/tex]

Anyone got any tips, is it my definitions of should I look closer at my algebra?

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