(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

At time t=0 hydrogen atom is in state

[tex]\psi(r,0)=\frac{4}{(2a)^{3/2}}[e^{-r/a}+iA\frac{r}{a}e^{-r/2a}(-iY^{1}_{1}+Y^{-1}_{1}+\sqrt{7}Y^{0}_{1})][/tex]

a) Is it possible to normalize wave function ?

b) Find [tex]\psi(r,t)[/tex] if at time t=0 measuring [tex]L_{z}[/tex] we find [tex]\hbar[/tex]

2. Relevant equations

3. The attempt at a solution

a)

Using eigenstates of hydrogen I can write[tex]\psi(r,0)[/tex] as

[tex] \psi(r,0) = \frac{4\sqrt{\pi}}{2^{^3/2}}\varphi_{100} + 4\sqrt{3}A\varphi_{211}-4\sqrt{21}Ai\varphi_{210}-4\sqrt{3}Ai\varphi_{21-1}[/tex]

Normalization condition [tex]\sum|c_{n}|=1[/tex] gives me [tex]A^{2}=\frac{1-2\pi}{432}[/tex] or [tex]A=\sqrt{\frac{2\pi-1}{432}}i[/tex] , but this does not satisfy normalization condition since I assumed that A is real.

I could assume that A is complex, but then I would get two unknowns (A=x+iy).

So I would say that it is not possible to normalize wave function.

If my answer is correct can someone explain this to me on practical example, do I need more information for normalizing ? where do I get it ? by measurment ?

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# Homework Help: Normalizing Hydrogen wavefunction

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