Uncertainty Principle of Heisenberg

The initial enthusiasm for the Bohr model of the atom began to fade soon after its introduction. New discoveries in modern physics indicated that Bohr s ideas needed to be modified. The Bohr model of the hydrogen atom pinpointed both the electron s energy and its distance from the nucleus at exactly the same time. However, the Uncertainty Principle of Heisenberg required that if the energy of the electron is known exactly there must be uncertainty concerning its location. Both could not be known exactly at the same time. 

For most gas molecules, there are several hundreds, even thousands, of possible molecular energy states. Therefore, one expects to find a large number of wavelengths at which the molecules absorb the incident energy, which makes the prediction of gas absorption a very difficult problem. Additionally, each of these absorption wavelengths can be broadened because of pressure and temperature as well as the uncertainty principle of Heisenberg. It is obvious that exact consideration of all these active frequencies/wavelengths may not be... 

A simple particle collision is described as a particle current exchanging an interaction boson with another similar current. The appearance of an extra boson is made possible by the uncertainty principle of Heisenberg which implies that for sufficiently short times and distances the conservation laws of energy and momentum can be violated AE At > hl2 and Ap Ax > h 2, where AA means a small uncertainty or deviation ia A A = E, p, t, x), Eand p are the energy and momentum of the particle, t and x are time and spatial coordinates. The smallness of the reduced (sometimes called rationalized) Planck constant, h = 1.055 x 10 Js ensures that in the macroworld the conservation laws are exactly fulfilled. The exchanged boson maybe real or virtual depending on whether or not the conservation laws are fulfilled for its creation if it is real, then it is emitted and so it can be detected if it is virtual, then it is absorbed and one can see the result of the boson exchange only, i.e., the effect of the interaction on the motion of the particles involved. 

The measured half-life of the state is 89.4 ps, which corresponds to a energy width, T, or AE, due to the Heisenberg uncertainty principle of ... 

Werner Heisenberg, bom Wurzburg, Germany, 1901. Ph.D. Munich, 1923. Professor, Leipzig University, Max Planck Institute. Nobel Prize 1932 for his famous uncertainty principle of 1927. Director of the German atomic bomb/reactor project 1939-1945. Held various scientific administrative positions in postwar (Western) Germany 1945-1970. Died Munich 1976. 

Using the position and momentum space entropies, Bialynicki-Birula and Mycielski [109] derived a stronger version of the Heisenberg uncertainty principle of quantum mechanics. The entropy sum, in D-dimensions, satisfies the inequality [110]... 

If the excited state of a nucleus has a mean life-time, r, there will be a spread of the y-ray energy, Ey, resulting from the decay of this nucleus, due to the Heisenberg uncertainty principle, of width, T, at half height ... 

The Heisenberg uncertainty principle offers a rigorous treatment of the qualitative picture sketched above. If several measurements of andfi are made for a system in a particular quantum state, then quantitative uncertainties are provided by standard deviations in tlie corresponding measurements. Denoting these as and a, respectively, it can be shown that... 

The electromagnetic spectrum is a quantum effect and the width of a spectral feature is traceable to the Heisenberg uncertainty principle. The mechanical spectrum is a classical resonance effect and the width of a feature indicates a range of closely related r values for the model elements. 

From the Heisenberg uncertainty principle as stated in Equation (1.16) estimate, in cm and Hz, the wavenumber and frequency spread of pulsed radiation with a pulse length of 30 fs, typical of a very short pulse from a visible laser, and of 6 ps, typical of pulsed radiofrequency radiation used in a pulsed Fourier transform NMR experiment. 

Early in the twentieth century physicists established that molecules are composed of positively charged nuclei and negatively charged electrons. Given their tiny size and nonclassical behavior, exemplified by the Heisenberg uncertainty principle, it is remarkable (at least to me) that Eq. (1) can be considered exact as a description of the electrostatic forces acting between the atomic nuclei and electrons making up molecules and molecular systems. Eor those readers who are skeptical, and perhaps you should be skeptical of such a claim, I recommend the very readable introduction to Jackson s electrodynamics book [1]. 

In the earlier treatment we reached the conclusion that resonance absorption occurs at the Larmor precessional frequency, a conclusion implying that the absorption line has infinitesimal width. Actually NMR absorption bands have finite widths for several reasons, one of which is spin-lattice relaxation. According to the Heisenberg uncertainty principle, which can be stated... 

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