@ion201 @andrewdurkiewicz @orbeckst As far as the integral of the fourier transform goes, we can use an approximation on the assumption that the particle's position is discretized at all times meaning that the sum is not continues and some positions are unknown. Therefore, we can use a discrete fourier transform and since the fourier series is a limit of the fourier transform we can just use one of the intergrating techniques learned earlier in the semester like the trapezoid or simpson which is just a series from a to b sampled N times. This is key because instead of integrating from -inf to +inf we simply integrate from zero to K where K is the total momentum shift if hbar is set to one, and this method also gives a localized in space fourier transform or series. From here we just define our integrals for before magnet, inside of magnet, and after magnet with the appropriate if statements for the time intervals as described in the literature.
orbeckst
commented
8 years ago
@ion201 @andrewdurkiewicz @orbeckst As far as the integral of the fourier transform goes, we can use an approximation on the assumption that the particle's position is discretized at all times meaning that the sum is not continues and some positions are unknown. Therefore, we can use a discrete fourier transform and since the fourier series is a limit of the fourier transform we can just use one of the intergrating techniques learned earlier in the semester like the trapezoid or simpson which is just a series from a to b sampled N times. This is key because instead of integrating from -inf to +inf we simply integrate from zero to K where K is the total momentum shift if hbar is set to one, and this method also gives a localized in space fourier transform or series. From here we just define our integrals for before magnet, inside of magnet, and after magnet with the appropriate if statements for the time intervals as described in the literature.