The same analytical expression gets inconsistent FourierTransform results - Mathematica Stack Exchange most recent 30 from mathematica.stackexchange.com 2019-09-19T16:08:09Z https://mathematica.stackexchange.com/feeds/question/34027 https://creativecommons.org/licenses/by-sa/4.0/rdf https://mathematica.stackexchange.com/q/34027 8 The same analytical expression gets inconsistent FourierTransform results Leo Fang https://mathematica.stackexchange.com/users/7101 2013-10-14T23:49:13Z 2015-06-10T22:53:15Z <p>I have an expression which is just a linear combination of plane waves, and I'd like to calculate FT of it. I know what I will get should be a bunch of delta functions, but it turns out <em>Mathematica</em> gives me a completely wrong result:</p> <pre><code>FourierTransform[(E^(-I (k1 + k2) (x1 + x2)) (E^(I (k2 x1 + k1 x2)) + E^(I (k1 x1 + k2 x2))))/(4 \[Pi] (I + 2 k1 - 2 w) (-I - 2 k2 + 2 w)), {x1, x2}, {p1, p2}] </code></pre> <blockquote> <pre><code>0 </code></pre> </blockquote> <p>However, if I re-organize the numerator of this expression to a simpler form of plane waves</p> <pre><code>E^(-I (k1 + k2) (x1 + x2)) (E^(I (k2 x1 + k1 x2)) + E^(I (k1 x1 + k2 x2))) // ExpandAll </code></pre> <blockquote> <pre><code>E^(-I k2 x1-I k1 x2)+E^(-I k1 x1-I k2 x2) </code></pre> </blockquote> <p>and then insert the above expression back to the numerator, after <code>FourierTransform</code> I get the correct result:</p> <pre><code>FourierTransform[(E^(-I k2 x1 - I k1 x2) + E^(-I k1 x1 - I k2 x2))/ (4 \[Pi] (I + 2 k1 - 2 w) (-I - 2 k2 + 2 w)), {x1, x2}, {p1, p2}] </code></pre> <blockquote> <pre><code>(DiracDelta[-k2+p1] DiracDelta[-k1+p2])/(2 (I+2 k1-2 w) (-I-2 k2+2 w))+(DiracDelta[-k1+p1] DiracDelta[-k2+p2])/(2 (I+2 k1-2 w) (-I-2 k2+2 w)) </code></pre> </blockquote> <p>So the question is: is it a bug or what? </p>