Probability and integration – Mathematica Stack Exchange


ClearAll("Global`*")

 time = Solve(x - (1/2)*g*(t^2) == 0, t)



 position = Solve(x - (1/2)*g*(t^2) == 0, x)

 v = D((g t^2)/2, t)

 T = Sqrt(2*h/g)

 dt = D((Sqrt(2) Sqrt(x))/Sqrt(g), x)

 Ptdt1 = dt1/T // PowerExpand

 Ptdt = 
 Replace(Ptdt1, {t -> (Sqrt(2) Sqrt(x))/Sqrt(g), 
   dt1 -> (1/(Sqrt(2) Sqrt(g) Sqrt(x)))*dx}, All)



 rhot = Ptdt/Ptdt((2))

 Integrate(rhot, {x, 0, h})

 Ex = Integrate(x*rhot, {x, 0, h})

 h = 20



 Plot(rhot, {x, 0, h}, AxesOrigin -> {0, 0})

ss

Please see my code to do a problem in Griffith’s quantum mechanics. But I have a feel that my code is really lengthy and is not general. Is there a way to make this general? or any easy alternatives?
solution