Heisenburg uncertainty principle

Heisenburg uncertainty principle For small particles which possess both wave and particle. properties, it is impossible to determine accurately both the position and momentum of the particle simultaneously. Mathematically the uncertainty in the position A.v and momentum Ap are related by the equation... 

For DBES data three main factors contribute to the S parameter in polymers (1) free-volume content, (2) free-volume size, and (3) chemical composition. First, larger free-volume content contributes to a larger S value. DBES measures radiation near 511 keV where a major contribution comes from p-Ps. This p-Ps contribution is only 1/3 the o-Ps intensity as that in I3 of PAL data. Second, when p-Ps is localized in a defect with a dimension fix, the momentum Ap has a dispersion according to the Heisenburg uncertainty principle AxAp > h/4n. The S parameter from DBES spectra is a direct measure of the quantity of momentum dispersion. In a larger size hole where Ps is localized, there will be a larger S parameter due to smaller momentum uncertainty. Therefore, in a system with defects or voids, such as polymers, the S parameter is a qualitative measure of the defect size and defect concentration. The value of the S parameter also depends on the momentum of the valence electrons, which annihilate with the positrons. The absolute value of the S parameter therefore, may differ from polymer to polymer. Third, the S parameter depends on the electron momentum of the elements. As the atomic number of the elements increases, the electron momentum increases, and thus the S parameter decreases. Fortunately, in chemicals of... 

The rate constants for both the forward and reverse processes are those of unimolecular processes (units s ), and it is the slowest of these two processes that we must compare with the rate at which the system is interrogated. For spectroscopic determinations, the timescale of the analytical technique is dictated by the Heisenburg uncertainty principle. The energy gap (A ) between the two states connected by the absorption is related to the time difference At by (26)... 

---