Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Normalization of Radial wavefunction of hydrogen atom

  1. Jul 21, 2012 #1
    All I need to evaluate the normalization coefficient. I need a step by step guide. It will be a great help if someone please tell me where can i get the solution (with intermediate steps). I think the solution can be done using the orthogonal properties of associated Laguerre polynomial. I need the steps. Thanks.

    Attached Files:

  2. jcsd
  3. Jul 21, 2012 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

  4. Jul 24, 2012 #3
    thanks a lot. the book contains the solution. but i still have one more confusion. the radial wavefunction (normalized) in the book has a minus sign. but i found many places where the minus sign has not been included. though the probability density requires the mod square of ψ, i want to know the shape of ψ. hence, what is the real value of it? should i include minus sign?

    Attached Files:

  5. Jul 24, 2012 #4


    User Avatar
    Science Advisor

    Wavefunctions are always uncertain up to a phase. So you can multiply the wavefunction by -1, or in fact by any number of the form exp(i * phi) where phi is any real value, without changing any observables.
  6. Jul 24, 2012 #5
    i have an equation,
    f(ρ) = [itex]\rho^{l+1}[/itex][itex]e^{-\rho}[/itex][itex]\upsilon(2\rho)[/itex]

    i want to transform it to the following multiplying only the right hand side with [itex](-1)^{2l+1}[/itex][itex](2)^{l+1}[/itex],
    f(ρ) = [itex](-1)^{2l+1}[/itex][itex](2\rho)^{l+1}[/itex][itex]e^{-\rho}[/itex][itex]\upsilon(2\rho)[/itex]

    is it possible?

    i want to use [itex](2\rho)^{l+1}[/itex] instead of [itex]\rho^{l+1}[/itex], because, the normalization coefficient normalizes with respect to ρ whatever the the function f(ρ) is. and [itex](2)^{l+1}[/itex] is not a function of ρ.

    i want to multiply by [itex](-1)^{2l+1}[/itex], because i found that if the associated Laguerre polynomial is [itex]AL^{2l+1}_{n+l}(x)[/itex]=[itex]\frac{d^{2l+1}}{dx^{2l+1}}[/itex][itex]L^{}_{n+l}(x)[/itex]. now, in some places, i found A=1 and other places [itex]A=(-1)^{2l+1}[/itex]. besides, is it something related to Condon-Shortley Phase factor?
    as after multiplyng by anything which is not a function of [itex]\rho[/itex] will still satisfy the associated laguerre differential equation, can i do this multiplication of [itex](-1)^{2l+1}[/itex][itex](2)^{l+1}[/itex]? thanks.
    Last edited: Jul 24, 2012
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook