Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Trouble with Laplace transform of a function

  1. Jan 11, 2014 #1
    I have a probability distribution as follows:


    \tilde{k}=\frac{2\pi k}{N}.

    \begin{equation}\sin\theta_k=\frac{1}{\sqrt{2}}\sin\frac{2\pi k}{N}.\end{equation}

    Can anyone please help me find the laplace transform of $p_j(t)$? I would also be glad if anyone could help me plot the probability distribution as a function of $j$ for fixed $N$ and $t$. Please note that the probability is zero for odd $j+t$. Thank You!
  2. jcsd
  3. Jan 12, 2014 #2


    User Avatar
    Gold Member

    I guess you need to expand all these expression until you end up with a sum of products like

    sin(Θk t) sin(Θk' t)

    The Laplace transform of this term is simple, but the sum still need to be simplified.
    I expect the result to be expressed as sum, but a closer form is not impossible.

    I this expression comes out of a piece of physics, it would be helpful to explain it here.
    The underlying physics could help to figure out the end result.
  4. Jan 12, 2014 #3
    Ok, this expression describes the probability distribution of a quantum random walker in a finite graph. And one more thing is that even Matlab cannot evaluate the laplace transform of this function. I do not need the detailed derivation of the result (although knowing it would be pretty cool), I just need the final result so that I can use it in another problem. Any help is highly appreciated.
  5. Jan 13, 2014 #4


    User Avatar
    Gold Member

    Should we read "sin(Θk t)" or "sin(Θk) t" ?
  6. Jan 13, 2014 #5
  7. Jan 13, 2014 #6


    User Avatar
    Gold Member

    This Laplace transform should be useful:

    [tex]L(Sin(a t) Sin(b t)) = \frac{2 a b p}{a^4+2 a^2 \left(p^2-b^2\right)+\left(b^2+p^2\right)^2}[/tex]
  8. Feb 7, 2014 #7
    Will matlab be able to handle this? I know we can find out laplace transform in matlab. I want to try out that, but when I type the above expression in matlab, I always get some error.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook