# Radial wave function of hydrogen (chart) Calculator

## Calculates a table of the electron radial wave functions of hydrogen-like atoms and draws the chart.

 The electron position r with the Bohr radius a = 1 unit is the distance from the nucleus.

 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 [ Initial position r of electron Increment , Repetition ]
 $\normal Probability\ density\ of\ finding\\\hspace{50}\ electron\ in\ a\ Hydrogen\ atom\\[10pt](1)\ -{\large\frac{\hbar^2}{\2m}}\nabla^2\psi-{\large\frac{Ze^2}{r}}\psi=E\psi\\\hspace{30}E=-{\large\frac{Z^2me^4}{2n^2\hbar^2}},\qquad Z=\{1:H,\ 2:He^+\}\\\hspace{30}\psi_{n,l,m}(r,\theta,\phi)=R_{nl}(r)Y_l^{m}(\theta,\phi)\\\vspace{10}(2)\ R_{nl}(r)=-\sqrt{({\large\frac{2Z}{na}})^3{\large\frac{(n-l-1)!}{2n(n+l)!}}}e^{-{\normal\frac{Zr}{na}}} \\\hspace{90}\times\ ({\large\frac{2Zr}{na}})^{l} L_{\small{n-l-1}}^{\small{2l+1}}({\large\frac{2Zr}{na}})\\\hspace{30}a={\large\frac{\hbar^2}{me^2}}\ :Bohr\ radius\\\vspace{10}(3)\ Probability\ density:\ R_{nl}(r)R_{nl}^*(r)r^2\\\hspace{20}{\large\int_{\small 0}^{\hspace{25}\small{\infty}}}R_{nl}R_{nl}^*(r)r^2dr=1\\$

Radial wave function of hydrogen (chart)
 [1-9] /9 Disp-Num5103050100200
[1]  2018/01/12 11:06   Male / Under 20 years old / High-school/ University/ Grad student / A little /
Purpose of use
Homework
[2]  2017/05/12 04:44   Male / 30 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
Calculation of phase shift
[3]  2015/02/27 03:32   Male / 40 years old level / Others / Very /
Purpose of use
Investigation of quantum formula for calculation of electron configurations.
[4]  2015/02/06 21:04   Female / 30 years old level / A teacher / A researcher / Very /
Purpose of use
Comment/Request
the units of r?
[5]  2014/08/21 01:53   Male / 30 years old level / A teacher / A researcher / A little /
Purpose of use
Wave function study
Comment/Request
What are the columns headed -R(r) and -rR(r) please, in relation to R, |R|**2 and 4PIr**2|R|**2 ?
[6]  2014/04/12 10:50   Male / 50 years old level / Others / A little /
Purpose of use
checking calculation
Comment/Request
Units of the calculation? r=1: r=1 Bohr radius? r=1 Angstroms?
from Keisan
The units of r, e, m and h are SI units.
[7]  2014/04/05 20:32   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Physics homework
[8]  2013/05/31 01:42   Female / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
having home work
[9]  2012/01/27 04:05   Male / 50 years old level / A teacher / A researcher / Very /
Purpose of use
inorganic chemistry

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