Heisenberg linewidth

The ultimate (minimum) linewidth of an optical band is due to the natural or lifetime broadening. This broadening arises from the Heisenberg s uncertainty principle, AvAt < U2jt, Av being the full frequency width at half maximum of the transition and the time available to measure the frequency of the transition (basically, the life-... 

Linewidth is governed by the Heisenberg uncertainty principle, which says that the shorter the lifetime of the excited state, the more uncertain is its energy ... 

Under these conditions the linewidth (z)E) of the emitted (and absorbed) radiation is governed by the Heisenberg Uncertainty Principle that is, AE = h/2 tit where h is Planck s radiation constant, and r is the mean... 

ESR is very useful in the study of dynamic properties of membrane components because of its high sensitivity and favorable time scale. Early ESR studies of short-range lateral diffusion in membranes were based on Heisenberg exchange (HE) effects of nitroxide spin-label line width. The HE contribution to the ESR linewidth is given for nitroxides by = )dDNACf, where d is the encounter dis-... 

Lattice vibration phonon energies Heisenberg natural linewidths (C,)... 

The possibly transferred rotational energy is considered as restricted according to Heisenbergs uncertainty relation AE=h/Tc > Erot Af /fc) by the lifetime of the collisional intermediate state. From this assumption Lc has been derived to 2, and only two free fit parameters remain The interaction time Xc, which is on the order of several femtoseconds, and Ao as constant linewidth per Amagat, which comprehends the temperature dependence of the base rates. 

Another important feature that influences the absorption linewidth is the length of time that an excited nucleus stays in the excited state. The Heisenberg uncertainty principle teUs us that ... 

According to the Bohr model of the atom, atomic absorption and emission linewidths should be infinitely narrow, because there is only one discrete value for the energy of a given transition. However, there are several factors that contribute to line broadening. The natural width of a spectral line is determined by the Heisenberg uncertainty principle and the lifetime of the excited state. Most excited states have lifetimes of s,... 

The total sampling period of the FID, known as the acquisition time, is ultimately dictated by the frequency resolution required in the final spectrum. From the Heisenberg s Uncertainty Principle, the resolution of two lines separated by Ai/ Hz requires data collection for at least 1/Ai/ s. If one samples the FID for a time that is too short, then the frequency differences cannot be resolved and fine stmcture is lost (the minimum linewidth that can be resolved is given approximately by 0.6/AQ). Likewise, if the signal decays rapidly then one is unable to sample it for a long period of time and again can resolve no fine stmcture. In... 

Due to the contribution of various broadening mechanisms, the linewidths typically observed in atomic spectrometry are significantly broader than the natural width of a spectroscopic line which can be theoretically derived. The natural width of a spectral line is a consequence of the limited lifetime r of an excited state. Using Heisenberg s uncertainty relation, the corresponding half-width expressed as frequency is ... 

Assume that all other line-broadening effects except the natural linewidth have been eliminated by one of the methods discussed in the previous chapters. The question that arises is whether the natural linewidth represents an insurmountable natural limit to spectral resolution. At first, it might seem that Heisenberg s uncertainty relation does not allow outwit the natural linewidth (Vol. 1, Sect. 3.1). In order to demonstrate that this is not true, in this section we give some examples of techniques that do allow observation of structures within the natural linewidth. It is, however, not obvious that all of these methods may realty increase the amount of information about the molecular structure, since the inevitable loss in intensity may outweigh the gain in resolution. We discuss under what conditions spectroscopy within the natural linewidth may be a tool that really helps to improve the quality of spectral information. 

Continuing from remarks ( 62)-( 63), the following conclusion can be drawn The formula t F = h is often used for the estimation of the natural linewidth. This formula is sometimes interpreted as the time-energy equivalent of the Heisenberg relation, where r is the uncertainty (standard deviation) of the lifetime and F (FWHM) is that of the energy state. It should be stressed, however, that while r can play the assigned role (because the standard deviation is equal to the expected value in the case of the exponential distribution), the quantity F cannot be interpreted as standard deviation, since the Cauchy distribution does not have any. 

Since the relaxation determines the lifetime, At, of a spin state, the Heisenberg Uncertainty Principle relates it to the uncertainty of the Zeeman eigenvalues, E and Ei, thereby allowing this phenomenon to affect the linewidth of EPR signals, as these depend inversely on T. ... 

The theoretical linewidth in resonance experiments is determined by the Heisenberg uncertainty relation. In ABMR the width is determined by the time spent by the atoms in the oscillating field and corresponds to 10-50... 

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