Timeline for Does the Fourier transform apply for any number of dimensions?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 19, 2021 at 22:37 | vote | accept | Anders Gustafson | ||
| Aug 19, 2021 at 22:37 | comment | added | Anders Gustafson | Thank You for the information! | |
| Aug 19, 2021 at 19:55 | comment | added | J.G. | @AndersGustafson Yes, although we'd normally write it more concisely as$$\Psi(\vec{x})=(2\pi\hbar)^{-3/2}\int_{\Bbb R^3}e^{ip\cdot x/\hbar}\Phi(\vec{p})d^3\vec{p}.$$ | |
| Aug 19, 2021 at 19:25 | comment | added | Anders Gustafson | So does this mean that in 3d the equation becomes $$\Psi(x_1,x_2,x_3)=\frac{1}{(2\hbar\pi)^\frac{3}{2}}\int_{-\infty}^\infty\left(\int_{-\infty}^\infty\left(\int_{-\infty}^\infty\left({e^{i(p_1x_1+p_2x_2+p_3x_3)/\hbar}}\Phi(p_1,p_2,p_3)\right)dp_1\right)dp_2\right)dp_3$$? | |
| Aug 19, 2021 at 16:57 | history | answered | J.G. | CC BY-SA 4.0 |