3 ms·
Note that you are wrong, it doesn't become classical mechanics for small sharp wave functions. It has similar movement, but the wave function would also thin ou
by username90 7y ago
Note that you are wrong, it doesn't become classical mechanics for small sharp wave functions. It has similar movement, but the wave function would also thin out until it is smoothed out over the entire universe. We all know particles doesn't do that, hence schrödinger equation alone isn't enough to explain observations about classical mechanics.
- scotty79 7y agoCould you elaborate on that? How do we know particles don't do that? Being high near one spot and smooth, near zero over entire rest of universe looks exactly like a particle to me.
- username90 7y agoNo, I mean it will be evenly spread out in all directions and not have any location where it is dense.
- scotty79 7y agoI don't see what you are saying in the description of Erhenfest theorem. They are saying: "For general systems, if the wave function is highly concentrated around a point [... the thing different between classical and quantum ...] will be almost the same, since both will be approximately equal to [...]. In that case, the expected position and expected momentum will approximately follow the classical trajectories, at least for as long as the wave function remains localized in position."
- kgwgk 7y ago> at least for as long as the wave function remains localized in position." The problem is that, as he said, “the wave function would also thin out until it is smoothed out over the entire universe”.
- scotty79 7y agoIs this then consequence of Schrodinger equation? How fast does that happen? Would the photon from remote galaxy be significantly spread out? How can we know it is not? Is the effect you are talking about the one described here: https://en.m.wikipedia.org/wiki/Free_particle https://en.m.wikipedia.org/wiki/Free_particle in section "Spread of a wave packet"?
- kgwgk 7y agoSee also https://en.m.wikipedia.org/wiki/Wave_packet#Gaussian_wave_packets_in_quantum_mechanics https://en.m.wikipedia.org/wiki/Wave_packet#Gaussian_wave_pa... “For example, if an electron wave packet is initially localized in a region of atomic dimensions (i.e., 10−10 m) then the width of the packet doubles in about 10−16 s. Clearly, particle wave packets spread out very rapidly indeed (in free space): For instance, after 1 ms, the width will have grown to about a kilometer.” “Note that a very narrow initial wave packet instantly becomes infinitely wide, but with a phase which is more rapidly oscillatory at large values of x. This might seem strange — the solution goes from being localized at one point to being "everywhere" at all later times, but it is a reflection of the enormous momentum uncertainty of a localized particle, as explained above.”
- scotty79 7y agoI see but what about particles that are not that precisely localised and don't have such extreme uncertainity of momentum? It's very logical that a particle that might have any momentum quicky spreads out to be smoothly everywhere. Particle with not that precise position and not that uncertain momentum should stay fairly comapct for large amount of time.
- kgwgk 7y agoWhat does “fairly compact” mean if not “precisely localised”? If the wave function is not localized it doesn’t make much sense to talk about a particle in the first place.