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    I have a question that says;

    A particle living in one spatial dimension has a wavefunction (function f(x) in this case) given by;

     f(x) = Ae^{-|x|/a}

    It asks me to find the normalisation constant, so I ASSUMED you would take limits over infinity and minus infinity and integrate  |f(x)|^{2} , with that equal to one. If I do this I get

     [\frac {-A^{2}ae^{-2|x|/a}}{2}] = 1 with limits infinity and minus infinity.

    As you can tell, that answer just gives me zero on the left hand side. What exactly am I meant to do?
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    You need to consider x > 0 and x <0 separately.
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    (Original post by Scipio90)
    You need to consider x &gt; 0 and x &lt;0 separately.
    Right, do you mean integrate with limits infinity to 0, and 0 to minus infinity then add them together? I've checked that and it still gives me zero <_>;
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    Yes. Post your working.
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    (Original post by Scipio90)
    Yes. Post your working.
     [\frac {-A^{2}ae^{-2|x|/a}}{2}] limits infinity and 0 is;

     [\frac {-A^{2}ae^{-2|\infty|/a}}{2} - \frac {-A^{2}ae^{-2|0|/a}}{2}] = [0 - \frac {-A^{2}a}{2}] = [\frac {A^{2}a}{2}]

     [\frac {-A^{2}ae^{-2|x|/a}}{2}] limits 0 to minus infinity is;

     [\frac {-A^{2}ae^{-2|0|/a}}{2} - \frac {-A^{2}ae^{-2|-\infty|/a}}{2}] = [\frac {-A^{2}a}{2} - \frac {-A^{2}ae^{-2|\infty|/a}}{2}] = [\frac {-A^{2}a}{2} - 0] =  [\frac {-A^{2}a}{2}]

    Which added together just becomes zero.
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    Sketch e^-|x|. Is your answer for the <0 part sensible?
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    (Original post by Scipio90)
    Sketch e^-|x|. Is your answer for the &lt;0 part sensible?
    Aye, the previous question asked me to sketch the wave equation. It's reflected in the y-axis meaning the area should be double of what is on either side. But why am I getting zero :|. I have a feeling that the integration of e^-2|x|/a is different to what I've put.
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    Aye yes, my integral is wrong. I'll have it sorted soon. Thanks a lot for your help
 
 
 
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