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Normalizing a wave function

  1. Jan 20, 2017 #1
    1. The problem statement, all variables and given/known data
    "assume that the three real functions ψ1,ψ2, and ψ3 are normalized and orthogonal. Normalize the following function"

    ψ1 - ψ21/(sqrt2) + ψ3sqrt(3)/sqrt(6)



    2. Relevant equations
    This is for a physical chemistry class. I haven't seen an example like this. All that is in our textbook is that integral[ /ψ/2dT] needs to equal 1 which is accomplished by adjusting N so N2 Integral[ /ψ/2dx] =1

    3. The attempt at a solution
    Is this correct? What range do I integrate it over? no x values are given.


    Any help will be greatly appreciated!
     
  2. jcsd
  3. Jan 20, 2017 #2

    vela

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    Is what correct? You haven't shown any work.

    The readability of your post would improve if you use LaTeX. Here's a primer: https://www.physicsforums.com/help/latexhelp/.
     
  4. Jan 20, 2017 #3
    I don't know why all my subscripts disappeared.

    ψ1 - ψ2 1/(sqrt6) + ψ3 sqrt(3)/sqrt(6)

    In the book it says that to normalize a function you need to adjust N so that
    N2 Integral [/ψ/2 dx] =1

    I don't know how I'd apply that to this question
     
  5. Jan 20, 2017 #4

    vela

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    In this problem, you have ##\psi(x) = N\left(\psi_1 - \frac{1}{\sqrt{6}} \psi_2 + \frac{\sqrt{3}}{\sqrt{6}}\psi_3\right)##. (Are you sure about that state? It's written a bit strangely, i.e., ##\sqrt{3}/\sqrt{6} = 1/\sqrt{2}##.)
     
  6. Jan 20, 2017 #5
    That's how it's written in the book.

    Since x isn't in the function
    That's just how it's written. So when I integrate that with respect to x i get N(ψ1 - ψ2 1/(sqrt6) + ψ3 sqrt(3)/sqrt(6))x +C
    Did I integrate that correctly? And if so what do I do from here?
     
  7. Jan 20, 2017 #6

    vela

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    Remember that ##\psi_1##, ##\psi_2##, and ##\psi_3## are functions of ##x##. You said the normalization condition is
    $$\int_{-\infty}^\infty \psi^2\,dx = 1.$$ You want to substitute the expression you're given for ##\psi## and evaluate the integral.

    Think about what it means when you're told that the ##\psi_i##'s are normalized and orthogonal to each other.
     
  8. Jan 20, 2017 #7
    Ohhh! I did it as an indefinite integral. So, just to clarify, I need to plug in the whole original equation in to the integral?
     
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