Do Quantum Particles Jump Rather Than Move?

[cree_be_mee]

[Forked off from this thread to allow for discussion of more basic principles of QM]

Time derivatives limit the mechanism for evolution in a system. Since quantum particles jump rather than move through space, a rate of change of position per unit time is meaningless. Indeterminacy arises in this conflict between trying to force a particle to move through space when it wants to jump. IE. It won't have a range of velocities so you're just dividing by zero to get the position.

 

[mfb]

Since quantum particles jump rather than move through space

There are no "jumps" in quantum mechanics: the equations and the evolution of the wave function are continuous.
There is a momentum operator, apart from the mass as factor this is a velocity of the particles. It doesn't have to take a single value, however.

Indeterminacy arises in this conflict between trying to force a particle to move through space when it wants to jump.

This is just nonsense.

 

[cree_be_mee]

There are no "jumps" in quantum mechanics: the equations and the evolution of the wave function are continuous.

So how does an electron get from R_1s to R_2p? Or are you saying that there are continuous bands of emission?

 

[Nugatory]

So how does an electron get from R_1s to R_2p? Or are you saying that there are continuous bands of emission?

As far as the mathematical formalism of quantum mechanics is concerned, the electron doesn't "get from" one orbital to another. You need quantum electrodynamics to completely describe the process, but in a sort of hand-waving way we could say that an electron disappeared from the 1s orbital at about the same time that another electron appeared in the 2p orbital.

More often we don't apply all of this machinery. The wave function is a linear combination (also called a "superposition") of two of the eigenstates of time-independent Schrodinger's equation (google for "hydrogen atom Schrodinger" to see how this works), and it is evolving continuously and deterministically according to the time-dependent equation. The wave function gives us the probability of finding "the" electron in the 1s or 2p states at any given time.

 

[jtbell]

Note that the wave functions for the two orbitals overlap significantly in a spatial sense.

http://hyperphysics.phy-astr.gsu.edu/hbase/hydwf.html#c1

So there's no need for the electron to "jump" in position.

Note also that whether the electron even has a definite position before we measure it is a matter of interpretation of the mathematics of QM. There are interpretations which go either way on this question. But they all make the same predictions for things that we can actually measure, and they all have features that some people (different people for different interpretations!) consider to be "weird." So the choice comes down to personal philosophical preference. That doesn't prevent people from arguing about them anyway. Hang around here long enough and you're sure to see such arguments eventually.

 

[cree_be_mee]

and it is evolving continuously and deterministically according to the time-dependent equation. The wave function gives us the probability of finding "the" electron in the 1s or 2p states at any given time.

Okay so what I said was that an electron cannot follow a spacetime trajectory. What you said is that there's a continuous probablility of finding the electron "there". But having a deterministic probability isn't the same as having a deterministic position.

 

[bhobba]

Okay so what I said was that an electron cannot follow a spacetime trajectory.

That's entirely interpretation dependant. Some interpretations have it with a trajectory - others do not.

QM is in fact silent about such things.

It doesn't say it jumps etc etc - its a theory about the results of observations (without going into the detail of exactly what an observation is - if you want to pursue that start a new thread). What happens when not observed its silent about.

Thanks
Bill

 

[DrChinese]

But having a deterministic probability isn't the same as having a deterministic position.

Quantum position and momentum are not deterministic, and in fact they are not simultaneously well defined in any ordinary sense. The Heisenberg Uncertainty Principle describes their relationship.