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

2021 ◽  
Author(s):  
Jixin Chen
Keyword(s):  
Energy Density ◽  
Distribution Functions ◽  
Wave Functions ◽  
Classical Solutions ◽  
Complementary Energy ◽  
Density Distributions ◽  
Space And Time ◽  
Classical Wave ◽  
Energy Distribution Functions ◽  
Complex Distribution Function

<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>

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

2021 ◽  
Author(s):  
Jixin Chen
Keyword(s):  
Energy Density ◽  
Distribution Functions ◽  
Wave Functions ◽  
Classical Solutions ◽  
Complementary Energy ◽  
Density Distributions ◽  
Space And Time ◽  
Classical Wave ◽  
Energy Distribution Functions ◽  
Complex Distribution Function

<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>

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

2021 ◽  
Author(s):  
Jixin Chen
Keyword(s):  
Energy Density ◽  
Distribution Functions ◽  
Wave Functions ◽  
Classical Solutions ◽  
Complementary Energy ◽  
Density Distributions ◽  
Space And Time ◽  
Classical Wave ◽  
Energy Distribution Functions ◽  
Complex Distribution Function

<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>

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

2021 ◽  
Author(s):  
Jixin Chen
Keyword(s):  
Energy Density ◽  
Distribution Functions ◽  
Wave Functions ◽  
Classical Solutions ◽  
Complementary Energy ◽  
Density Distributions ◽  
Space And Time ◽  
Classical Wave ◽  
Energy Distribution Functions ◽  
Complex Distribution Function

<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>

scholarly journals Wavefront dislocations reveal the topology of quasi-1D photonic insulators

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Clément Dutreix ◽  
Matthieu Bellec ◽  
Pierre Delplace ◽  
Fabrice Mortessagne
Keyword(s):  
Local Density ◽  
Topological Defects ◽  
Wave Functions ◽  
Topological Classification ◽  
Local Density Of States ◽  
Topological Phase Transition ◽  
Interference Fringes ◽  
Classical Wave ◽  
Phase Singularities

AbstractPhase singularities appear ubiquitously in wavefields, regardless of the wave equation. Such topological defects can lead to wavefront dislocations, as observed in a humongous number of classical wave experiments. Phase singularities of wave functions are also at the heart of the topological classification of the gapped phases of matter. Despite identical singular features, topological insulators and topological defects in waves remain two distinct fields. Realising 1D microwave insulators, we experimentally observe a wavefront dislocation – a 2D phase singularity – in the local density of states when the systems undergo a topological phase transition. We show theoretically that the change in the number of interference fringes at the transition reveals the topological index that characterises the band topology in the insulator.

Electron Energy Distribution Functions of Hydrogen: The Effect of Superelastic Vibrational Collisions and of the Dissociation Process

1979 ◽  
Vol 34 (5) ◽  
pp. 585-593 ◽  
Author(s):  
M. Capitelli ◽  
M. Dilonardo
Keyword(s):  
Boltzmann Equation ◽  
Energy Distribution ◽  
Electron Energy ◽  
Distribution Functions ◽  
Electron Energy Distribution ◽  
Hydrogen Atoms ◽  
Dissociation Process ◽  
Excitation Rate ◽  
The Boltzmann Equation ◽  
Energy Distribution Functions

Abstract Electron energy distribution functions (EDF) of molecular H2 have been calculated by numerically solving the Boltzmann equation including all the inelastic processes with the addition of superelastic vibrational collisions and of the hydrogen atoms coming from the dissociation process. The population densities of the vibrational levels have been obtained both by assuming a Boltz-mann population at a vibrational temperature different from the translational one and by solving a system of vibrational master equations coupled to the Boltzmann equation. The results, which have been compared with those corresponding to a vibrationally cold molecular gas, show that the inclusion of superelastic collisions and of the parent atoms affects the EDF tails without strongly modifying the EDF bulk. As a consequence the quantities affected by the EDF bulk, such as average and characteristic energies, drift velocity, 0-1 vibrational excitation rate are not too much affected by the inclusion of superelastic vibrational collisions and of parent atoms, while a strong influence is observed on the dissociation and ionization rate coefficients which depend on the EDF tail. Calculated dissociation rates, obtained by EDF's which take into account both the presence of vibrationally excited molecules and hydrogen atoms, are in satisfactory agreement with experimental results.

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