Rethinking the Boundary Conditions in the Particle-in-a-Box Mind Experiment

<p>In this manuscript, I speculated that the energy density distributions along space and time in a quantum system are uniform. Thus, the complementary energy contributions are added to the classical solutions of the 1D particle in a box problem, making the energy density a complex distribution function over space and time. Then the concept is extended to the free rotation problem with a Hamiltonian slightly different than the classical Schrödinger equation. The picturized energy distribution functions and associated time evolution are described in movies for comparison between example classical wave functions and the energy density functions. The wave functions for the hydrogen atom are then guessed based on the historical solutions.</p><p><br></p>

Rethinking the Boundary Conditions in the Particle-in-a-Box Mind Experiment

<p>In this manuscript, I speculated that the energy density distributions along space and time in a quantum system are uniform. Thus, the complementary energy contributions are added to the classical solutions of the 1D particle in a box problem, making the energy density a complex distribution function over space and time. Then the concept is extended to the free rotation problem with a Hamiltonian slightly different than the classical Schrödinger equation. The picturized energy distribution functions and associated time evolution are described in movies for comparison between example classical wave functions and the energy density functions. The wave functions for the hydrogen atom are then guessed based on the historical solutions.</p><p><br></p>

Rethinking the Boundary Conditions in the Particle-in-a-Box Mind Experiment

<p>In this manuscript, I speculated that the energy density distributions along space and time in a quantum system are uniform. Thus, the complementary energy contributions are added to the classical solutions of the 1D particle in a box problem, making the energy density a complex distribution function over space and time. Then the concept is extended to the free rotation problem with a Hamiltonian slightly different than the classical Schrödinger equation. The picturized energy distribution functions and associated time evolution are described in movies for comparison between example classical wave functions and the energy density function.</p>

Rethinking the Boundary Conditions in the Particle-in-a-Box Mind Experiment

<p>In this manuscript, I speculated that the energy density distributions along space and time in a quantum system are uniform. Thus, the complementary energy contributions are added to the classical solutions of the 1D particle in a box problem, making the energy density a complex distribution function over space and time. Then the concept is extended to the free rotation problem with a Hamiltonian slightly different than the classical Schrödinger equation. The picturized energy distribution functions and associated time evolution are described in movies for comparison between example classical wave functions and the energy density function.</p>

Transport Characteristics of the Electrification and Lightening of the Gas Mixture Representing the Atmospheres of the Solar System Planets

Electrification represents a fundamental process in planetary atmospheres, widespread in the Solar System. The atmospheres of the terrestrial planets (Venus, Earth, and Mars) range from thin to thick are rich in heavier gases and gaseous compounds, such as carbon dioxide, nitrogen, oxygen, argon, sodium, sulfur dioxide, and carbon monoxide. The Jovian planets (Jupiter, Saturn, Uranus, and Neptune) have thick atmospheres mainly composed of hydrogen and helium involving. The electrical discharge processes occur in the planetary atmospheres leading to potential hazards due to arcing on landers and rovers. Lightning does not only affect the atmospheric chemical composition but also has been involved in the origin of life in the terrestrial atmosphere. This paper is dealing with the transport parameters and the breakdown voltage curves of the gas compositions representing atmospheres of the planets of the Solar System. Ionization coefficients, electron energy distribution functions, and the mean energy of the atmospheric gas mixtures have been calculated by BOLSIG+. Transport parameters of the carbon dioxide rich atmospheric compositions are similar but differ from those of the Earth’s atmosphere. Small differences between parameters of the Solar System's outer planets can be explained by a small abundance of their constituent gases as compared to the abundance of hydrogen. Based on the fit of the reduced effective ionization coefficient, the breakdown voltage curves for atmospheric mixtures have been plotted. It was found that the breakdown voltage curves corresponding to the atmospheres of Solar System planets follow the standard scaling law. Results of calculations satisfactorily agree with the available data from the literature. The minimal and the maximal value of the voltage required to trigger electric breakdown is obtained for the Martian and Jupiter atmospheres, respectively.

Rate coefficients for electron-impact dissociation of O3+ to singly charged fragments

Rate coefficients for electron-impact dissociation of O3+ to the O+ and O2+ fragments are calculated for the new, recommended cross section data set and for various collisional conditions. Two sets of the cross section data, measured recently by different experimental groups, are used. These cross sections differ significantly with each other, but are renormalized and optimized to the coherent data base. Rate coefficients for the ozone cation fragmentation are determined using the Maxwellian and the non-thermal electron energy distribution functions (EEDF). In the case of Maxwellian distribution, mean electron energies cover the range from zero up to 2 keV. Non-thermal electron energy distribution functions are adopted from the recent electron observations by the 3-D plasma and energetic particles experiment on the WIND spacecraft. The non-thermal rates are evaluated for the mean electron energies from 4 to 80 eV. The role of the possible contribution of electron-impact dissociation of O3+ to the Ozone layer depletion has been emphasized.