Timeline for Reason for $(2 \pi \hbar)^{-\frac{3}{2}}$ prefactor for quantum mechanical wavepacket
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 28, 2018 at 17:55 | vote | accept | Gjert | ||
| Nov 28, 2018 at 17:54 | comment | added | Gjert | Great explanation, thank you! Also, it's a bit off topic, but could you lead me in the direction of how the momentum operator was motivated? I've tried looking for it in Classical Mechanics book, but just states it as a definition without reasoning. | |
| Nov 28, 2018 at 17:47 | comment | added | eranreches | The power comes from the dimensionality of the problem. In general, in $d$ dimensions the power is $\frac{d}{2}$. Note that $\hbar$ also appears because in your case the integration variable is $p$ instead of $k$. | |
| Nov 28, 2018 at 17:42 | comment | added | Gjert | If $\hbar$ is for units, is there a special reason for $\hbar^{-3/2}$? I understand the $(2\pi)^{-3/2}$ from the def. of Fourier transforms, but not sure where $\hbar$ is coming from. | |
| Nov 28, 2018 at 17:37 | history | answered | Sean E. Lake | CC BY-SA 4.0 |