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The homogeneous strength of the Higgs field 
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#37
Nov913, 06:09 PM

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"The electron zips around in an orbit."  No, it's position has a steady state probability distribution. "The electron spends part of the time within the nucleus."  No, it has a certain constant probability of being found there. "Alpha decay happens because the alpha particle repeatedly bounces against the Coulomb barrier, and eventually penetrates it."  Again no, its wavefunction has a certain constant amplitude at the barrier. These are all examples of an important difference between Classical and Quantum Mechanics. 


#38
Nov1013, 01:02 AM

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You make it sound as if the only purpose of QM is to solve the timeindependent Schroedinger equation (in my opinion this is not quite true). But even if you focus on the resulting steadystate probability functions, you will see that they often contain timelike parameters, for example an angular frequency or a velocity. So the static solution already hints at underlying dynamics.
"The electron zips around in an orbit."  No, it's position has a steady state probability distribution. Of course that is true. But it is also true that the orbiting electron has a welldefined nonzero kinetic energy and velocity. Therefore it (or something) is moving! This is one of the amusing paradoxes of QM. In fact, if the electron where nonmoving, one would run into serious problems. For example, for the outer orbits (higher quantum numbers) of the atom there would be no comparison possible between the quantum orbits and their classical counterparts, where the electron moves around the nucleus in a planetlike elliptical orbit. 


#39
Nov1013, 05:52 AM

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#40
Nov1013, 07:44 AM

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However its absolute value (normally referred to as SPEED) is certainly nonzero. 


#41
Nov1013, 07:46 AM

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That's why I said "velocity" and not "speed".



#42
Nov1013, 12:07 PM

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Why does the electron have a nonzero speed? Because in the subatomical realm things move! This has been recognized by countless leading physicists. It is also the insight that led Mr. Schroedinger to formulate his famous result: the timedependent Schroedinger equation. Its keyaspect is that it is a DYNAMICAL equation. It describes the evolution (in space and time) of the wave function of a particle, in relation to its initial state (t=0). Necessarily the equation contains parameters that are associated with time, such as Planck' s constant and the inertial mass of the particle.
Technically it is very useful to consider first the solutions to the timeindependent Schroedinger equation. This is a convenient simplification. This way one obtains the energy eigenfunctions. They form (mathematically speaking) a basis, and so they can be superimposed to create timedependent functions. But my point is, that the solutions of the timeindependent Schroedinger equation contain exactly the same parameters as the timedependent version. So no wonder that inspection of the steadystate solutions reveals certain dynamical properties of the particle, such as its average speed in orbit. In my view this property is no less "physically real" than the probability density. 


#43
Nov1013, 02:55 PM

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No one ever questioned that particles can move in quantum mechanics in general. The main point was that they do not move around in timeindependent states, which are solutions to the timeindependent SE.



#44
Nov1013, 04:58 PM

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No one disputes the existence of timeindependent states, which are solutions of the timeindependent SE.
The discussion is how the electron can have a nonzero speed while being in a timeindependent state. 


#45
Nov1013, 05:11 PM

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A nonzero expectation value for the speed.
It does not have a welldefined, single "speed value". I don't see the problem. 


#46
Nov1013, 06:09 PM

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#47
Nov1013, 06:42 PM

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Wikipedia statement: "The mean speed of the electron in hydrogen is 1/137th of the speed of light."
Therefore the electron is moving. Yet its probability distribution is timeindependent. I don't have a problem reconciling these two (seemingly contradictory) facts. For me it obvious that the electron is moving. Due to the impossibility to have information on the position of the electron, the best one can do is to assume that it is simultaneously present at the different positions allowed in the orbital. Of course with proper weighting. This leads to the timeindependent solution, in which the effects of motion becomes hidden. 


#48
Nov1113, 12:47 PM

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Anyway, Bill_K is right. Please start a new thread if you want to discuss interpretations of the wavefunction as "moving" or "not moving". 


#49
Nov2813, 10:42 AM

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The purpose of Physics Forums is to promote interesting and helpful discussions, but in reality these are scarce and occur only within the inner circle of experts. 


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