Quantum mechanics observation problems

I. Gilary, A. Fleischer, N. Moiseyev, Calculations of time-dependent observables in non-Hermitian quantum mechanics The problem and a possible solution, Phys. Rev. A 72 (2005) 012117/1. 

The LevinthaTs paradox is an open problem still. To avoid the core of the problem — it s kinema-tical aspect — we propose a new approach in this regard. Actually, we treat the macromolecules conformations as the quantum-mechanical observable. Bearing in mind the foundations of the decoherence theory, we are able to model both, existence and maintenance of the conformations as well as the conformational transitions in the rather short time intervals. Our model is rather qualitative yet a general one — while completely removing the LevinthaTs paradox — in contradistinction with the (semi-)classical approach to the issue. 

Molecular modeling has evolved as a synthesis of techniques from a number of disciplines—organic chemistry, medicinal chemistry, physical chemistry, chemical physics, computer science, mathematics, and statistics. With the development of quantum mechanics (1,2) ia the early 1900s, the laws of physics necessary to relate molecular electronic stmcture to observable properties were defined. In a confluence of related developments, engineering and the national defense both played roles ia the development of computing machinery itself ia the United States (3). This evolution had a direct impact on computing ia chemistry, as the newly developed devices could be appHed to problems ia chemistry, permitting solutions to problems previously considered intractable. 

The prominent position of quantum mechanics led a coterie of academic theoreticians to think that their approach could solve research problems facing the pharmaceutical industry. These theoreticians, who met annually in Europe and on Sanibel Island in Florida, invented the new subfields of quantum biology [45] and quantum pharmacology [46]. These names may seem curious to the uninitiated. They were not meant to imply that some observable aspect of biology or pharmacology stems from the wave-particle... 

Since TD-DFT is applied to scattering problems in its QFD version, two important consequences of the nonlocal nature of the quantum potential are worth stressing in this regard. First, relevant quantum effects can be observed in regions where the classical interaction potential V becomes negligible, and more important, where p(r, t) 0. This happens because quantum particles respond to the shape of K, but not to its intensity, p(r, t). Notice that Q is scale-invariant under the multiplication of p(r, t) by a real constant. Second, quantum-mechanically the concept of asymptotic or free motion only holds locally. Following the classical definition for this motional regime,... 

In cases where both the system under consideration and the observable to be calculated have an obvious classical analog (e.g., the translational-energy distribution after a scattering event), a classical description is a rather straightforward matter. It is less clear, however, how to incorporate discrete quantum-mechanical DoF that do not possess an obvious classical counterpart into a classical theory. For example, consider the well-known spin-boson problem—that is, an electronic two-state system (the spin) coupled to one or many vibrational DoF (the bosons) [5]. Exhibiting nonadiabatic transitions between discrete quantum states, the problem apparently defies a straightforward classical treatment. 

Although solving the Schrodinger equation can be viewed as the fundamental problem of quantum mechanics, it is worth realizing that the wave function for any particular set of coordinates cannot be directly observed. The quantity that can (in principle) be measured is the probability that the N electrons are at a particular set of coordinates, ri,...,rjv. This probability is equal to i x (r. r,v)v f(r., rN), where the asterisk indicates a complex conju-... 

Even with the assurance that quantum mechanics has firm underpinnings in experimental observations, students learning this subject for the first time often encounter difficulty. Therefore, it is useful to again examine some of the model problems for which the Schrodinger equation can be exactly solved and to learn how the above rules apply to such concrete examples. 

These were bold and simple statements. To put them in a modern context, the discovery of triphenylmethyl combined the novelty of something like bucky balls with the controversial nature of something like polywater or cold fusion. Thus Gomberg was soon to find that the triphenylmethyl problem was attractive and complex enough to occupy him and many others for a long time. A first period lasted until about 1911 when the phenomena observed had been clarified to the satisfaction of a majority of the research community. Theoretically, little understanding was possible before the advent of the electron pair bond and, in particular, theory based on quantum mechanical concepts. This meant that the theory available... 

In simple English, this implies that if you were in a 4-D universe and launched planets toward a sun, the planets would either fly away to infinity or spiral into the sun. (This is in contrast to a (3 + 1) universe that obviously can, for example, have stable orbits of moons around planets.) A similar problem occurs in quantum mechanics, in which a study of the Schrodinger equation shows that the hydrogen atom has no bound states for n > 5. This seems to suggest that it is difficult for higher universes to be stable over time and contain creatures that can make observations about the universe. 

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