The Correspondence Principle and the Idea of Balanced Reactions
| Main Author: | Francesco R. Ruggeri |
|---|---|
| Format: | info publication-preprint |
| Terbitan: |
, 2019
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/2639001 |
Daftar Isi:
- In bound state quantum mechanics, high energy eigenvalues are said to lead to a density W(x)W(x) where W(x) is the wavefunction, whose envelope approaches the classical value 1/v(x), where v(x) is the classical velocity given by sqrt[2m(E-V(x)]. For the quantum oscillator, the ground state mimics classical statistical mechanics, while the high energy states mimic classical mechanics. For both classical statistical mechanics and classical physics, we argue in this note that one may use a reaction picture to derive probabilities. Traditionally, the classical density 1/v(x) is obtained from dx = v dt or dx/v = dt with “dt” being proportional to probability. In classical statistical mechanics, one has two particle scattering and imposes a balance using P(p1)P(p2)=P(p3)P(p4). In the case of V(x), one may also write a reaction equation (1) showing particles leaving and entering a little box. In this note, it we argue it would be good to have a consistent picture when dealing with densities, namely a reaction picture, with “breakup or decay” balancing “synthesis”. We then try to argue that such a reaction picture may actually also apply to high energy eigenvalue quantum mechanical bound states.