Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.
Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.
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I am a tech graduate - and a nonnative speaker of English.
I have a question about the basis of q.mechanics.
I know there are ywo variants of Schrod. equation: one for the free motion particle - under the action of no force - and another version for the particle subjected to a force. My understanding was these two versions are not related in any way. One thing happens for the particle if there is no force which acts upon the it, another thing happens if there is a force. This means these two formulas of the prob. function (or wave function) are established in two different physical circumstances: in one case here is a force in another one there is not. So why there are these simple cases treated in the textbooks in which in the same time(in the same situation) the particle is not subjected to a force and it is subjected to a force (even if this happens in different space domains. The two events are what is known in prob. theory contrary events - the existence or not of a potential field in the space surrounding the particle. If these two cases are merged in one case then the Schrod eq. does not provide a base to say that there must be one single continous funtion defined upon the entire spatial domain.) ? I don`t see any base to support the assumption one could the merger these two cases: why the prob. function should satisfy both equations ?the first eq assumes the etire space has no force: f it is the prob.function of particle p beeing located at every place at every time when there is no force in entire space, not in an arbitrary domain. the same with second case - the eq. satisfied by the prob. function of a particle being located in potential field which spreads in universe.
otherwise how would I know the function resulted from the merger of these cases is a continous one ?
more clear I hope. Lets assume one determines the prob function when the particle is free. The partcile appears somwhere in the space and starts behaving like the prob.function f1 says. Suddenly a force field appears somewhere. The physical seting ia new one: one does not have a free motion particle moving in a free universe. But one does not also have a particle moving a filed force universe - and maybe not even in a force field if at first the part. is outside the field. In these circumstances, one has a physicl case not covered by the theory before: the theory deals with what happens in two different and not related cases and misses this third one. wy there mst be a continus function now ? Schrod eq. works if either the part. is exclusively in a free motion state or exclusively in a force field motion state not with both cases in the same time...
Last edited by frgn1 (2009-11-01 09:48:41)
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In conection with the above question:
what kind of probabbility is used to measure the probability of a particle to be located in (xyz) at (t): clasical, frequentist - the limit of the big number frequency, subjectivist. IN practice one needs to choose from these types pf measures of the probabbility. In case one chooses a measure which requires for instance many experiments which are these experiments and how many of them could be performed ?
From the few things I have read in several quantum physics texts, it appears no one performed these experiments to determine such a function and if this function works in practice. maybe I am wrong
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