Statistical Considerations of the Schrodinger Equation Based on Local Energy Conservation
| Main Author: | Francesco R. Ruggeri |
|---|---|
| Format: | info publication-preprint |
| Terbitan: |
, 2018
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/1492699 |
Daftar Isi:
- We argue that the ideas of quantum mechanics can be obtained statistically, if one suggests that the motion of a particle (or the combination of the particle moving to the right and left with momentum p) is governed by a function g(x,p) which seems to imply that the particle is not simply translating. If there were simple translation, there would be no need for x dependence. If one considers an average of the kinetic energy of many g(x,p) and sets this equal to an average kinetic energy at x with proper space dependent normalization, then this should be part of an energy conservation equation at each point x i.e. KEave(x)+V(x)=E. The normalization factor of g(x,p) in such an average, namely W(x)= sum over p (g(x,p)ap) with ap as weights can then be shown to be a candidate for the following relationship: density(x)=W(x)W(x). Furthermore, it can be argued that g(x,p) is periodic in x and by using the form d\dx d(x) * (probability momentum), one may argue that g(x,p) takes on the form of sin(px) or cos(px). In such a case, g(p,x) terms in W(x) coincide with a Fourier series of W(x). It is suggested that g(p,x) may have physical meaning if one considers models of a moving particle which involve zitterbewegung. In such a case, there is not simply translation. It has also been pointed out, that there are issues with a straightforward interpretation of the probability continuity equation for quantum mechanics as W(x) includes interference.