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Quantum Transport in Semiconductor Systems
Published in Dragica Vasileska, Stephen M. Goodnick, Gerhard Klimeck, Computational Electronics, 2017
Dragica Vasileska, Stephen M. Goodnick, Gerhard Klimeck
The Born interpretation of quantum mechanics enables us to determine probabilistic information from a wave function. For example, we can answer the following question: In an ensemble measurement of position at time t, what is the probability that a member of the ensemble will exhibit a value in the range from x to x þ dx? To characterize the results of an experiment, we use two statistical quantities: the ensemble average, 〈x〉, and the standard deviation, Δx. In quantum theory, the ensemble average of an observable for a particular state of the system is called the expectation value of that observable, calculated as
Interpretational Issues in Quantum Mechanics
Published in F.J. Duarte, Quantum Optics for Engineers, 2017
There is a plethora of interpretations of quantum mechanics. Among the most prominent interpretations one finds are the Copenhagen interpretation and the many-worlds interpretation. Albeit this is an interesting area of discussion, from the pragmatic perspective of physics, interpretations are not necessary to solve problems or predict the result of an experiment.
Pre-Born–Oppenheimer molecular structure theory
Published in Molecular Physics, 2019
Relying on the probabilistic interpretation of quantum mechanics, the structure of H was visualised as a proton shell (Figure 5) with the protons found at around the antipodal points, and HD was seen as a proton shell and a deuteron shell within which the relative position of the three nuclei is dominated by a triangular arrangement (Figure 6). This analysis has demonstrated that elements of molecular structure can be recognised in the appropriate marginal probability densities calculated from the full electron-nuclear wave function. At the same time, a chemist would rather think about H as a (classical) rotating dumbbell (Figure 7) and HD as a (nearly) equilateral triangle. Although elements can be recognised in the probability density functions, the link to the classical structure which chemists have used for more than a century to understand and design new reaction pathways for new materials, is not obvious [97,99,100,102,121, 122].
Effect of confinement and external mechanical force on the cleavage of the bond in a diatomic molecule
Published in Molecular Physics, 2023
Ruchi Jha, Pratim Kumar Chattaraj
A quantum fluid density functional theory (QFDFT) has been developed by amalgamating time-dependent DFT and quantum fluid dynamics (QFD). Following generalised nonlinear Schrodinger equation (GNLSE) (also known as the so-called ‘Deb- Chattaraj equation’ [6]) is the backbone of QFDFT and it can also be derived using the stochastic interpretation of quantum mechanics [7]: