Timeline for $\hbar \rightarrow 0$ in quantum mechanics
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 28, 2015 at 0:15 | comment | added | WillO | @UnlimitedDreamer: You can think of quantum mechanics as a collection of theories, one for each value of $\hbar$. One of those theories happens to fit the data we see in the world we live in, but all of the theories are perfectly consistent. It makes perfect sense to consider the entire family of theories, to consider paths in the moduli space for those theories, and to take limits along those paths. | |
| Sep 27, 2015 at 22:39 | comment | added | Jold | @UnlimitedDreamer We do the same sort of thing when we take $c \to \infty$ to get from relativistic equations to Newtonian equations. $c$ has a definite value, but by pretending it is infinite our equations become Newtonian. In the same way, when we pretend Planck's constant is zero our equations go from quantum to classical. Edit: Just realized this is an old question. Not sure why it popped up in my recent questions page. | |
| Apr 19, 2013 at 7:22 | comment | added | leongz | It is worth noting that when a dimensionful quantity like $\hbar$ is taken to be small, it means that it is small compared to some quantity of the same dimension in the system. | |
| Apr 19, 2013 at 6:48 | review | First posts | |||
| Apr 19, 2013 at 6:51 | |||||
| Apr 19, 2013 at 6:43 | comment | added | anna v | It is like focusing a microscope ( dimensions h_bar) and diminishing the magnification until it is zero. It is the relative sizes of h_bar and the size of uncertainty in momentum times space . When we are at even microns, let alone milimeters, and measurable everyday momenta the h_bar can be considered zero. | |
| Apr 19, 2013 at 6:42 | comment | added | Alex L | @UnlimitedDreamer That is exactly what we are doing. Of course it is just a trick, in the real world Planck's constant has a definite value. It just so happens that ignoring that value often gets rid of the "quantumness" of our model. | |
| Apr 19, 2013 at 6:35 | comment | added | user12906 | $\hbar\rightarrow 0$, it Seems that we are changing the planks constant? How can we limit on a constant? | |
| Apr 19, 2013 at 6:31 | vote | accept | CommunityBot | ||
| Apr 19, 2013 at 6:29 | history | answered | Alex L | CC BY-SA 3.0 |