Timeline for Zener breakdown - a quantum mechanical derivation

8 events

when toggle format	what		by	license	comment
Dec 26, 2022 at 10:56	history	edited	SchrodingersCat		edited tags
Dec 24, 2022 at 19:57	answer	added	grjj3		timeline score: 2
Dec 24, 2022 at 15:00	history	tweeted			twitter.com/StackPhysics/status/1606666007573053440
Dec 24, 2022 at 14:18	history	edited	grjj3	CC BY-SA 4.0	added 1227 characters in body
Dec 24, 2022 at 14:11	comment	added	grjj3		Indeed, that was my initial approach (getting rid of the vanishingly small $\kappa^4$ is reasonable and greatly simplifies the calculation), however it still doesn't yield the correct result. Moreover, you are still left with terms like $\frac{G^{2}\hbar^{2}}{4m}$ and $\frac{G^{4}\hbar^{4}}{64m^{2}\mathcal{E}^{0}}$ that shouldn't be omitted, but even if we do omit them I still fail to retrieve the desired result.
Dec 24, 2022 at 12:52	comment	added	Sebastian Riese		My approach would be to analyze the order of the terms in the quadratic equation and omit the ones that are small (e.g. the $\kappa^4$ term is negligible for sufficiently small $\kappa$). You can probably arrive at the same expression by reducing the solutions of the quadratic equation under those assumptions – (e.g. the $\hbar^2\epsilon /m$ term can be omitted if $\epsilon \ll \mathcal{E}^0$).
Dec 24, 2022 at 12:47	history	edited	grjj3	CC BY-SA 4.0	edited body
Dec 24, 2022 at 12:41	history	asked	grjj3	CC BY-SA 4.0