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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
    2018 Award

    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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