Applications of Quantum Mechanics
Quantum mechanics provides the basis for most fields of modern physics and there are many well advanced methods of practical solution of specific and topical problems
- PDF / 963,360 Bytes
- 54 Pages / 439.37 x 666.142 pts Page_size
- 84 Downloads / 241 Views
Applications of Quantum Mechanics
Introduction Quantum mechanics provides the basis for most fields of modern physics and there are many well advanced methods of practical solution of specific and topical problems. These methods which may be perturbative or nonperturbative, often are specific to the various disciplines, and it would go far beyond the scope of a textbook to discuss them extensively and in due detail. For instance, atomic and molecular physics make extensive use of variational calculus and of many-body techniques the latter of which are of great importance also for the physics of condensed matter and for nuclear physics. Elementary particle physics, in turn, makes use of covariant perturbation theory as well as of various kinds of nonperturbative approaches. There are numerous methods to treat scattering off composite targets at low, intermediate, and high energies (optical potential, Green function techniques, eikonal approximation). Exact solutions are often approximated by numerical procedures such as integration of differential equations, diagonalization of large matrices in truncated Hilbert spaces, discretization and simulation by means of Monte Carlo methods, etc., which are adapted for the problem one wishes to study. In this chapter we first sketch the possible application of quantum mechanics to information theory. We then discuss nonrelativistic perturbation theory in its time independent and its time dependent versions. Finally, we give an introduction to selected techniques for treating systems of many interacting fermions. Relativistic, Lorentz covariant perturbation theory will be dealt with in Part Two.
5.1
Correlated States and Quantum Information
The principles of quantum mechanics were formulated and laid down in Chap. 3. In particular, the description of quantum states by means of statistical operators or, equivalently, by density matrices was discussed in detail and illustrated by a number of instructive examples. So one might be tempted to say that there is little to be added to what we worked out in Chap. 3, from the point of view of basic principles, and all F. Scheck, Quantum Physics, DOI: 10.1007/978-3-642-34563-0_5, © Springer-Verlag Berlin Heidelberg 2013
255
256
5 Applications of Quantum Mechanics
there is left to do is to develop practical methods for solving concrete problems of quantum mechanics which go beyond the few exactly solvable ones. Although the practical methods often are by no means simple and open up a wide field reaching far into modern research, the basic principles and the interpretation of quantum mechanics, after some further reflection, have perplexing consequences which often are different from expectations based on classical physics and which are testable in experiment. This is why we insert, as a first application, a discussion of nonlocalities in quantum mechanics, correlations, entangled states, as well as a short excursion to quantum information. All of these are topics of modern research and one should expect to see rapid progress fo
Data Loading...
