# Electron wave function of hydrogen Calculator

## Calculates the electron wave functions of hydrogen-like atoms.

 The wave function Ψ(r,θ,φ) is the solution to the Schrodinger equation.The angle unit of θ and φ are degrees.

 Atomic number Z H(1)He+(2) Principal quantum number n n=1,2,3,... Angular quantum number l l=0,1,2,..,n-1 Magnetic quantum number m m=-l,l+1,..,l-1,l Electron position r Bohr radius a=1 Zenith angle θ degree Azimuth angle φ degree 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit Ψ(r,θ,φ) rΨ(r,θ,φ)
 $\normal The\ wave\ function\ \psi(r,\theta,\phi)\\\hspace{100}of\ the\ Hydrogen\ atom\\[10pt](1)\ -{\large\frac{\hbar^2}{\2m}}\nabla^2\psi-{\large\frac{Ze^2}{r}}\psi=E\psi\\\hspace{25}E=-{\large\frac{Z^2me^4}{2n^2\hbar^2}},\qquad Z=\{1:H,\ 2:He^+\}\\\vspace{10}(2)\ \psi_{n,l,m}(r,\theta,\phi)=R_{nl}(r)Y_l^{m}(\theta,\phi)\\\hspace{10}{\large\int_{\small 0}^{\hspace{25}\small{\infty}}\int_{\small 0}^{\hspace{25}\small{\pi}}\int_{\small 0}^{\hspace{25}\small{2\pi}}}\psi_{\small{n,l,m}}\psi_{\small{n',l',m'}}\ r^2sin\theta drd\theta d\phi\\\hspace{80}=\delta_{\small{nn'}}\delta_{\small{ll'}}\delta_{\small{mm'}}\\\vspace{10}(3)\ R_{nl}(r)=-\sqrt{({\large\frac{2Z}{na}})^3{\large\frac{(n-l-1)!}{2n(n+l)!}}}e^{-{\normal\frac{Zr}{na}}} \\\hspace{90}\times\ ({\large\frac{2Zr}{na}})^{l}L_{n-l-1}^{2l+1}({\large\frac{2Zr}{na}})\\[15]\hspace{18}Y_l^m(\theta,\phi)=\sqrt{{\large\frac{2l+1}{4\pi}}{\large\frac{(l-m)!}{(l+m)!}}}P_l^m(cos\theta)e^{im\phi}\\$

Electron wave function of hydrogen
 [1-3] /3 Disp-Num5103050100200
[1]  2012/05/31 02:23   Male / Under 20 years old / Others / A little /
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Comment/Request
Can you explain how to calculate it on your own? (Preferably in a way a sixth grader like me could understand)
[2]  2012/05/04 23:14   Male / 20 years old level / A student / Very /
Purpose of use
schrodinger solutions
[3]  2009/07/27 10:55   Male / 50 level / A researcher / Very /
Purpose of use
Demonstration & Verification
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Very Good

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