China 
Africa 
Explore chapters and articles related to this topic
Basics of Classical Mechanics
Published in Alexander Bagaturyants, Vener Mikhail, Multiscale Modeling in Nanophotonics, 2017
Alexander Bagaturyants, Vener Mikhail
We start from classical mechanics for many reasons. The first and evident reason is that it forms the basis of molecular dynamics simulations. The second reason is that an understanding of quantum chemistry is impossible without addressing classical mechanics. This reason is deeply rooted in the essence of quantum chemistry as a science. Quantum chemistry can be considered as an application of quantum theory to chemistry. In fact, quantum chemistry was developed by physicists (W. Heitler and D. London [1]) in their daring attempt to explain the nature of chemical bonds in the simplest chemical molecule H2. Subsequently, quantum chemistry in many respects developed as an application of quantum mechanics to chemical and, par excellence, molecular problems. By now, computational molecular quantum mechanics (including methods and applications) still remains one of the main areas of quantum- chemical activity. Hence, quantum mechanics is one of the main foundations of quantum chemistry, and studying quantum chemistry is impossible without knowledge of the basics of quantum mechanics. However, according to the correspondence principle, the basics of quantum mechanics and quantum-mechanical equations cannot be properly formulated and fully understood without classical mechanics. Hence, the second reason is now evident.
The Rutherford–Bohr Atom
Published in Mario Bertolotti, The History of the Laser, 2004
Bohr’s papers on atomic structure started a great activity in many research centres, and Bohr himself contributed with further progress. A very important concept he developed to treat quantum problems, and that nobody better than him knew how to apply, was the ‘Correspondence Principle’ that relates predictions of classical theory with quantum theory. As Planck’s quantum formula for long wavelengths is well approximated by the classical Rayleigh formula, so Bohr argued that the classical mechanical frequency of rotation of the electron along its orbit, for very large orbits, should be well approximated by the formulae given by the classical laws. This allowed him to find rules—called selection rules—that established that not all transitions could take place, and to discover between which orbits transitions were allowed, therefore establishing the first criteria to predict which frequencies could be emitted (among the many corresponding to the different energy jumps). The rules also facilitated predictions of the light intensity corresponding to each possible transition to be made.
Applications of Schrödinger Equation: Potential (Quantum) Wells
Published in Zbigniew Ficek, Quantum Physics for Beginners, 2017
Problem 8.4 Show that, as n → ∞, the probability of finding a particle between x and x + Δx inside an infinite potential well is independent of x, which is the classical expectation. This result is an example of the correspondence principle that quantum theory should give the same results as classical physics in the limit of large quantum numbers.
Recent Developments in Cybernetics, from Cognition to Social Systems
Published in Cybernetics and Systems, 2019
Stuart A. Umpleby, Tatiana A. Medvedeva, Vladimir Lepskiy
The Correspondence Principle was proposed by Niels Bohr (1913) when developing the quantum theory. It says, “Any new theory should reduce to the old theory to which it corresponds for those cases in which the old theory is known to hold.” Wladyslaw Krajewski in a book on the Correspondence Principle (1977) expressed the view that a more general theory is not sufficient. There should also be a new dimension that was previously not noticed or had been thought to be insignificant. So, how could the role of the observer be formulated as a new dimension?