Quantum Physics Quantum Physics Help Forum

 May 19th 2016, 08:33 AM #1 Member   Join Date: Dec 2012 Location: Boulder, Colorado Posts: 63 Question about wave function spreading and shrinking My (limited) understanding of QM has been that, if you measure the position of a free electron (no forces on it) with an idealized precision (assumed zero error), then immediately after that measurement, the (position) wave-function psi(x) is a Dirac delta function, and the momentum wave-function phi(p) is a plane wave, indicating that the momentum has no definite value at that instant, but rather is in a superposition of all possible momenta, all weighted equally, and expressed as a plane wave. As time then progresses without any additional measurements being made, the Schrodinger equation for the position wave function psi(x) says (I think) that the delta function spreads out spatially as time increases. And I've always thought that the momentum wave function phi(p) starts to shrink as time progresses, i.e., the momentum plane wave becomes a wave packet whose width continuously decreases. I had always suspected that, in the limit as time goes to infinity, that the two wave function widths approach equality (in some sense) ... i.e., that the two quantities become "equally uncertain" at some "medium level" of uncertainty. That would be "nature's equilibrium" for (undisturbed) quantum objects. But if I haven't misunderstood Bohm (in his "Quantum Physics" book), he seems to say that, if (as opposed to the scenario above) you initially have the position wave function phi(x) as a plane wave, then the momentum has a definite value, and is conserved as time progresses (without any further measurements). I.e., he seems to be saying that the momentum always remains at that initial definite value, and the position always remains uniformly spread out. That seems to be inconsistent with my understanding of the first scenario. Was my original understanding incorrect, or am I misinterpreting Bohm? -- Mike Fontenot __________________ Mike Fontenot

 Tags function, question, shrinking, spreading, wave

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