Timeline for Continuity equation in QM
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 11, 2020 at 8:59 | comment | added | user | Thanks! Very helpful! | |
| Jun 11, 2020 at 8:06 | comment | added | Puk | What is special about $j$? The continuity equation tells you that it can be interpreted as the probability current: the rate of flow of probability per unit time per unit area. This is completely analogous to e.g. the electric current density, which satisfies the exact same equation, with $\rho$ replaced by the electric charge density. | |
| Jun 11, 2020 at 7:58 | comment | added | Puk | In 1D, it's even simpler. You just integrate within a fixed interval, and apply the fundamental theorem of calculus instead of the divergence theorem to get that result. The continuity equation says that the probability within a volume (left term) increases at the same rate probability is flowing into this volume (right term). No probability is being lost or no "new" probability generated. This also implies that the probability within all space is constant (equal to 1, of course). | |
| Jun 11, 2020 at 7:54 | comment | added | user | Thanks! In the one-dimensional case I suppose this reduces to "probability change + (current in -current out) =0". I just don't see how probability is conserved. It just seems like it is equal to some other quantity. What is special about this particular quantity ( ie probability current)? | |
| Jun 11, 2020 at 7:52 | history | answered | Puk | CC BY-SA 4.0 |