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B The deduction of Schrodinger equation, I'm stuck!

  1. Dec 26, 2017 #1
    Hi everyone! Please, I'm trying to understand the Schrodinger equation, and I've understood it this far, wich which is a miracle, hehehe:
    (Laplacian)(psi) plus ((2phi)/h)^2.2m (E-V)(psi)

    I know that hbar = h/(2phi)

    But how that turns into

    (Laplacian)(psi)+2m/(hbar)^2.(E-V)(psi)

    My math isn't good enough... =( can someone please point me how it happened? =)

    Thanks a lot!
     
  2. jcsd
  3. Dec 26, 2017 #2
    Or, in other words, how this:
    ∇^2Ψ+{[2π/h]^2}.2m(E-V)ψ

    Assuming

    ħ=h/2π

    Becomes

    ∇^2ψ+{2m/ħ^2}(E-V)Ψ

    Sorry for the bad English! =)

    Thanks!
     
  4. Dec 26, 2017 #3

    PeterDonis

    Staff: Mentor

    It might help if you would give a reference for where you are getting this from. I'm not sure what you are writing down is a correct expression for the Schrodinger Equation.

    Also, please use the PF LaTeX feature, it makes your equations much easier to read. See here for help:

    https://www.physicsforums.com/help/latexhelp/
     
  5. Dec 26, 2017 #4
    Thanks a lot! Sorry for the ugly equations!

    I'm based on this YouTube video:



    So, I'm starting with the Helmholtz equation:

    $$∇^2Ψ+(\frac {2π} {υ})^2Ψ$$

    And my goal is to the time independent Schrodinger equation

    ## - \frac {ħ^2} {2m} ∇^2 Ψ +VΨ = EΨ ##

    Miraculously, I 've kind of understood until here:

    ##∇^2 + (\frac {2π} {h})^2 . 2m (E-V)Ψ ##

    And I know that

    ## ħ= \frac {h} {2π} ##

    But I dont understand how that turned into this:

    ## ∇^2Ψ + \frac {2m} {ħ^2} (E-V)Ψ ##

    Please... Can someone please tell me what happened? I don't understand it... =(

    Thanks and sorry again for my confusion on the first and second posts!
     
  6. Dec 27, 2017 #5

    Demystifier

    User Avatar
    Science Advisor

    You must be missing something very very trivial, so trivial that it is very difficult to say what it is.
     
  7. Dec 27, 2017 #6
    Thanks everyone! I just woke and now I understood!

    ## ħ = \frac {h} {2π} ##
    That is the same as h = ħ2π

    Just substitute h for ħ2π in the first equation, cancel 2π, ^2 and multiply the 1 with 2m...

    Sorry to bother. Thanks all, funny how a night of sleep changes one's perspective.
     
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