Modern applications of the harmonic oscillator

Chadia Qotni, Hicham Laribou

In this work, we applied the invariant method to calculate the coherent state of the harmonic oscillator with position-dependent mass, which in modern physics has great application. We also obtain the calculation of Heisenberg’s uncertainty principle, and we will show that it is verified.

K. T. Hecht

Yu. V. Tsykareva, Dmitry N. Makarov

Abstract Quantum entanglement of coupled harmonic oscillators is frequently applied in quantum and non-linear physics, molecular chemistry and biophysics, which is why its study is of a great interest for modern physics. In this work a quantum entanglement of a coupled harmonic oscillator in a simple form was found. This simple form is presented as a single parameter – reflection coefficient R. All parameters of the studied system are included in the R coefficient. It is shown that the derivation of the expression can have applications in quantum optics, in particular in quantum metrology.

Mitchel Weissbluth

Horatiu Nastase

Written for a two-semester graduate course in Quantum Mechanics, this comprehensive text helps develop the tools and formalism of Quantum Mechanics and its applications to physical systems. It suits students who have taken some introductory Quantum Mechanics and Modern Physics courses at undergraduate level, but it is self-contained and does not assume any specific background knowledge beyond appropriate fluency in mathematics. The text takes a modern logical approach rather than a historical one and it covers standard material, such as the hydrogen atom and the harmonic oscillator, the WKB approximations and Bohr-Sommerfeld quantization. Important modern topics and examples are also described, including Berry phase, quantum information, complexity and chaos, decoherence and thermalization, nonstandard statistics, as well as more advanced material such as path integrals, scattering theory, multiparticles and Fock space. Readers will gain a broad overview of Quantum Mechanics, as solid preparation for further study or research.