scholarly journals The rotation of molecules in fields of octahedral symmetry

1936 ◽  
Vol 153 (880) ◽  
pp. 601-621 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Potential Energy ◽  
Potential Field ◽  
Rotational Energy ◽  
Dielectric Constants ◽  
Mathematical Treatment ◽  
Octahedral Symmetry ◽  
Specific Heats ◽  
Angular Coordinate ◽  
Energy States

A problem in quantum mechanics which has important applications in the theory of specific heats and dielectric constants of solids, is that of determining the rotational energy states of a molecule in a potential field, such as occurs in a crystal. A mathematical treatment of the rotation of molecules in crystals was first given by Pauling, and the theory has since been extended by several other authors. In these discussions, however, either the potential energy has been assumed to depend only on one angular coordinate or the term involving the second angular coordinate has been supposed to be sufficiently small to be treated as a perturbation.

scholarly journals The rotational energy-levels of a diatomic molecule in a tetrahedral field

1938 ◽  
Vol 164 (918) ◽  
pp. 420-435 ◽  
Author(s):  
H. M. Cundy ◽  
John Edward Lennard-Jones
Keyword(s):  
Potential Field ◽  
Special Form ◽  
Similar Case ◽  
Energy Levels ◽  
Point Group ◽  
Rotational Energy ◽  
Wave Functions ◽  
Octahedral Symmetry ◽  
Tetrahedral Symmetry ◽  
General Field

The rotation of molecules in fields with octahedral symmetry, which is an approximation to the fields in certain crystals, has been investigated by Devonshire (1936), in a paper in which he shows the types of the wave-functions for the general field of octahedral symmetry, and then obtains energy-levels for a particular field of this type. In this paper we shall use Devonshire’s method to determine the form of the wave-functions and energy-levels for the similar case when the potential field has not octahedral, but only tetrahedral symmetry, or complete ( A 1 ) symmetry of the four-point group T d . We shall again take a special form for the potential field, and show how the rotational levels split up as the field is increased, and also how the field modifies the wave-functions corresponding to the various levels.

Constructing Quantum Mechanics

2019 ◽  
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Stark Effect ◽  
Zeeman Effect ◽  
Black Body ◽  
Black Body Radiation ◽  
Wave Mechanics ◽  
Specific Heats ◽  
Old Quantum Theory ◽  
Upper Level

This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.

scholarly journals Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 125
Author(s):  
Tobias Gulden ◽  
Alex Kamenev
Keyword(s):  
Quantum Mechanics ◽  
Algebraic Topology ◽  
Riemann Surfaces ◽  
Surrounding Medium ◽  
Coulomb Systems ◽  
Dielectric Constants ◽  
Ion Interactions ◽  
Multivalent Ions ◽  
Electric Filed ◽  
Entropic Effects

We study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for the effective non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels.

scholarly journals Gravity to Electricity as Quantum

2020 ◽  
Author(s):  
Jong-hoon Lee
Keyword(s):  
Quantum Mechanics ◽  
Magnetic Fields ◽  
Potential Energy ◽  
Equilibrium State ◽  
Opposite Direction ◽  
Repulsive Force ◽  
The Earth ◽  
Gravity And Magnetic ◽  
The Relationship ◽  
Renormalization Theory

When gravity exists in magnetic fields, gravity interacts with magnetic fields to generate electricity Earth direction or opposite direction. In this experiment, we demonstrate it and explain why need the renormalization theory. And in this experimental model, the relationship between electricity, voltage and time were redefined through the analysis of data for 0.1 second. Voltage and time are in a 1: 1 matching relationship. The voltage can be recorded on the x-axis and time on the y-axis. It explains two expressions of the Schrödinger equation. According to these experiments, the electric potential energy generated in gravity and magnetic fields is not reflected in quantum mechanics. The renormalization theory has modified the quantum mechanics in four-dimensional systems. If gravity and electromagnetic force are particles, they are in a symmetrical balance of supersymmetric particles in the gravity generator. Gravity generator was voltage (0) and electricity (0) in Excel 6380 data of experiment F4 when it was in equilibrium state in the direction of the Earth by gravity force and in the opposite direction by the magnetic repulsive force.

What Is Light, Really?

2011 ◽  
Author(s):  
Sönke Johnsen
Keyword(s):  
Quantum Mechanics ◽  
Physical Properties ◽  
Quantum Entanglement ◽  
Uncertainty Principle ◽  
Modern Theory ◽  
Discrete Energy ◽  
Wave Particle Duality ◽  
The World ◽  
Energy States

This concluding chapter explains that the modern theory of light falls within the field of quantum mechanics. At first glance, quantum mechanics does not seem that strange—its name is based on the fact that light comes in units and that electrons have discrete energy states. It also includes the uncertainty principle, which states that one cannot know certain pairs of physical properties with perfect precision. Moreover, quantum mechanics involves the wave-particle duality of photons. The chapter then explores two of the most unusual aspects of quantum mechanics: two-slit interference and quantum entanglement. Both violate the most fundamental notions about how the world works.

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