Quantum Mechanics of the H2–H2 Interaction. IV. A Self‐Consistent Group Calculation with Strong Orthogonal Group Functions

1967 ◽  
Vol 47 (11) ◽  
pp. 4629-4641 ◽  
Author(s):  
V. Magnasco ◽  
G. F. Musso
Keyword(s):  
Quantum Mechanics ◽  
Orthogonal Group ◽  
Self Consistent ◽  
Consistent Group ◽  
Group Functions

The density matrix in may-electron quantum mechanics III. Generalized product functions for beryllium and four-electron ions

1963 ◽  
Vol 273 (1352) ◽  
pp. 103-116 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Density Matrix ◽  
Orthogonal Group ◽  
Electron Quantum ◽  
Group Functions ◽  
Strong Orthogonality

The theory of generalized product functions is extended to non-orthogonal group functions in the case of two groups. Calculations on beryllium and on some four-electron ions are based on such group functions, and are compared with similar calculations using orthogonal group functions. I t is shown that, in the case of the systems examined, the strong orthogonality restriction is not severe.

A LINEAR CORRELATION OF PROTON CHEMICAL SHIFTS IN SOME ALKYL CHLORIDES AND HYDROCARBONS WITH THE OCCUPATION NUMBER OF THE HYDROGEN ORBITALS

1965 ◽  
Vol 43 (12) ◽  
pp. 3188-3192 ◽  
Author(s):  
F. Hruska ◽  
G. Kotowycz ◽  
T. Schaefer
Keyword(s):  
Linear Correlation ◽  
Occupation Number ◽  
Chemical Shifts ◽  
The Self ◽  
Starting Values ◽  
Occupation Numbers ◽  
Self Consistent ◽  
Consistent Group ◽  
Proton Chemical Shifts ◽  
Group Orbital

A linear correlation exists between the proton shifts of some alkyl chlorides and some hydrocarbons and the occupation numbers of the hydrogen 1s orbitals in the C—H bonds. The occupation numbers are those given by the self-consistent group orbital and bond electronegativity method. The application of this correlation to the prediction of starting values for occupation numbers, to the derivation of bond anisotropies in ethylene and acetylene, and to the prediction of hydrogen-bonded shifts of C—H protons is discussed.

scholarly journals The Enigma of the Muon and Tau Solved by Emergent Quantum Mechanics?

2019 ◽  
Vol 9 (7) ◽  
pp. 1471
Author(s):  
Theo van Holten
Keyword(s):  
Quantum Mechanics ◽  
Droplet Model ◽  
Matter Waves ◽  
Equilibrium Configurations ◽  
Self Consistent ◽  
Usual Quantum ◽  
Electron Models ◽  
Charged Leptons ◽  
Emergent Quantum Mechanics

This paper addresses the long-standing question of how it may be explained that the three charged leptons (the electron, muon and tau particle) have different masses, despite their conformity in other respects. In the field of Emergent Quantum Mechanics non-singular electron models are being revisited, and from this exploration has come a possible answer. In this paper a deformable droplet model is considered. It is shown how the model can be made self-consistent, whilst obeying the laws of momentum and energy conservation as well as Larmor’s radiation law. The droplet appears to have three different static equilibrium configurations, each with a different mass. Tentatively, these three equilibrium masses were assumed to correspond with the measured masses of the charged leptons. The droplet model was tuned accordingly, and was thereby completely quantified. The dynamics of the droplet then showed a “De Broglie-like” relation p = K / λ . Beat patterns in the vibrations of the droplet play the role of the matter waves of usual quantum mechanics. The value of K , calculated by the droplet theory, practically equals Planck’s constant: K ≅ h . This fact seems to confirm the correctness of identifying the three types of charged leptons with the equilibria of a droplet of charge.

NONLINEAR QUANTUM MECHANICS WITH NONCLASSICAL GRAVITATIONAL SELF-INTERACTION II: NONSTATIONARY SITUATION

1993 ◽  
Vol 08 (16) ◽  
pp. 2683-2707 ◽  
Author(s):  
A. D. POPOVA ◽  
A. N. PETROV
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Variational Principles ◽  
Gravitational Interaction ◽  
Classical Field Theory ◽  
Classical Field ◽  
Stationary Case ◽  
Self Consistent ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

Quantum mechanics (first quantization) with self-consistent gravitational interaction, previously constructed for the stationary case, is extended to the general case. The two requirements for such a theory are realized: to obtain the theory maximally resembling a classical field theory and to achieve the invariance of the theory under the rescaling transformations of a wave function. The construction is not trivial, because it rejects the variational principles of extremality of any action and involves some principles of smoothed extremality which give relevant equations.

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