Normalizing a Wave Function

  • #1
1. [tex]Find \ C \ in \ terms \ of \ x_0 \ such \ that \ \psi(x,0) \ is \ normalized, \ where \ C \ and \ x_0 \ are \ constants.[/tex]
2. [tex]\psi(x,0)=Cexp\left (-\frac{\left |x \right |}{x_0} \right )[/tex]
3. [tex]\\ \psi(x,0)=Cexp\left (-\frac{\left |x \right |}{x_0} \right )\\
\Rightarrow \psi(x,0)=Cexp\left ( -\frac{x}{x_0} \right ) \ for \ x\geq 0 \\
and \ \psi(x,0)=Cexp\left ( \frac{x}{x_0} \right ) \ for \ x<0[/tex]


My thoughts were to split the absolute value up, but I am unsure. Also, I am unsure as to how to choose the bounds for normalizing. Should it just be over (-∞,+∞)?
 

Answers and Replies

  • #2
TSny
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The domain of the function should have been specified. If not, I think you are probably to assume (-∞,∞). It should be clear that the function (and its square) is an even function. So, the integral from -∞ to +∞ can be evaluated by taking twice the integral from 0 to infinity. Don't forget that it's the integral of the square of the function that should equal 1.
 

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