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zhillyz
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Homework Statement
The probablity density function of the [itex]n-state[/itex] of an electron is proportional to
[itex]f[/itex][itex]n[/itex][itex]=[/itex][itex](\frac{rz}{a_{0}})^{2n}[/itex][itex]e^ \frac{-2Zr}{\large na_{0}}[/itex]
show that the expectation value of the potential energy of the electron in
the [itex]n-th[/itex] quantum state of the hydrogen atoms is;
[itex]\frac{{-Z^2}{e^2}}{\large a_{0} n^2}[/itex]
For that do
(a) derive normalisation factor of the function. (5 marks)
(b) calculate the expectation value for [itex]<1/r>[/itex]. (5 marks).
(c) calculate the expectation value for [itex]< V >[/itex]. (5 marks).
You may use Mathematica or Mathcad for this exercise
Homework Equations
Normalization procedure
Take a function [itex]f(x)[/itex] and the Normalizing Constant as [itex]N[/itex] then
[itex]N^2∫f(x)*f(x) dx = 1[/itex]
and
[itex]N = \frac{1}{\sqrt{\large\int_o^\infty f(x)*f(x)}}[/itex]
The Attempt at a Solution
Put equation into mathematica then square it, then integrate it, then square root it and then divide function by answer?
If integrated from negative to positive infinity it should equal zero?
Wondering if my logic is okay before I move onto expectation values?