Theoretical physics IV. Quantum mechanics with problems in MAPLE

Leidy Lorena Alzate Vargas

A pathogen has the possibility to attack the human body causing diseases or epidemics depending of our defenses. Government and control health organizations have an especial interest in to know what the probability of the human is and a population to be attacked and infected by the pathogens and how it can be influenced by the virulence and concentration of the external agent or substance. In this way, physics has been involved in the solution of the problem giving to the global health institutions a guide to control the disease, by understanding the situation as a quantum phenomenon known as penetration of a potential barrier or as classical diffusion problem which involves the spatial and temporal variation of the concentration of the pathogen that causes the disease. The computations required to the solution of this problem are presented with MAPLE and is expected that this solutions have important implications to the global health care.

Marko Horbatsch, Daniel F. Styer, Susan R. McKay +1 more

Willi-Hans Steeb, Yorick Hardy

Solving problems in quantum mechanics is an essential skill and research activity for physicists, mathematicians, engineers and others. Nowadays, the labor of scientific computation has been greatly eased by the advent of computer algebra packages, which do not merely perform number crunching, but also enable users to manipulate algebraic expressions and equations symbolically. For example, the manipulations of noncommutative operators, differentiation and integration can now be carried out algebraically by the computer algebra package. This book collects standard and advanced methods in quantum mechanics and implements them using SymbolicC++ and Maxima, two popular computer algebra packages. Throughout, the sample programs and their outputs are accompanied with explanatory text of the underlying mathematics and physics explained in detail. Selected problems have also been implemented using two other popular packages Mathematica and Maple while some problems are implemented in C++. Modern developments in quantum theory are covered extensively, beyond the standard quantum mechanical techniques. The new research topics added to this second edition are: entanglement, teleportation, Berry phase, Morse oscillator, Magnus expansion, wavelets, Pauli and Clifford groups, coupled Bose Fermi systems, super-Lie algebras, etc.

Marko Horbatsch

A.V. Zorin, N. P. Tretyakov

The program is proposed for a realization of the symbolic algorithm based on the quantum mechanics with non-negative probability distribution function (QDF) and for calculations of energy levels for hydrogen-like atoms. The program is written up in the language MAPLE. In the framework of the algorithm an original Maple package for calculations of necessary functions, such as hydrogen wave functions, Sturmian functions and their Fourier-transforms, Clebsch-Gordan coefficients, etc. is proposed. Operators of observables are calculated on the basis of the QDF quantization rule. According to the Ritz method, eigenvalues of Ritz matrices represent spectral values of the quantity under investigation, i.e. energy. As an example, energy levels of hydrogen-like atoms are calculated and compared with experimental data retrieved from the NIST Atomic Spectra Database Levels Data. It turns out that this theory seems to be equivalent to the traditional quantum mechanics in regard to predictions of experimental values. However, the existence of a phase-space probabilistic quantum theory may be an important advance towards the explanation and interpretation of quantum mechanics.