Semiclassical phase space distributions and scattering theory of the harmonic oscillator and hydrogen atom

Jens Peder Dahl, Michael Springborg

We object to the proposal that the mapping of the three-dimensional hydrogen atom into a four-dimensional harmonic oscillator can be readily used to determine the Wigner phase-space distribution function for the hydrogen atom.

David Agmon, I. R. Senitzky

S. Nouri

In this work we present a theoretical study of the hydrogen atom in quantum phase space. A coordinate transformation is used that maps the hydrogen atom into a four-dimensional harmonic oscillator and the Wigner distribution function for the hydrogen atom is then obtained. This exactly soluble model can shed some light on finite-size features of Wigner's distribution, which will be a vital experience for various dynamic problems.

Shalom Shlomo, Manju Prakash

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.

Stanislav D. Tvorogov