A Practical Method for the Solution of Certain Problems in Quantum Mechanics by Successive Removal of Terms from the Hamiltonian by Contact Transformations of the Dynamical Variables Part I. General Theory

1942 ◽  
Vol 10 (8) ◽  
pp. 532-537 ◽  
Author(s):  
L. H. Thomas
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Practical Method ◽  
Contact Transformations ◽  
Successive Removal

Dualism QM and GR

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Noncommutative Geometry ◽  
Quantum Tunneling ◽  
Closed Surface ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Surface Integral ◽  
Definition Of

Quantum tunneling of noncommutative geometry gives the definition of time in the form of holography, that is, in the form of a closed surface integral. Ultimately, the holography of time shows the dualism between quantum mechanics and the general theory of relativity.

HYPER-SPHERICAL HARMONICS AND ANHARMONICS IN m-DIMENSIONAL SPACE

2008 ◽  
Vol 17 (06) ◽  
pp. 1125-1130
Author(s):  
M. R. SHOJAEI ◽  
A. A. RAJABI ◽  
H. HASANABADI
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Spherical Harmonics ◽  
Interaction Potential ◽  
Dimensional Space ◽  
Harmonic Polynomials ◽  
Central Importance ◽  
Computational Tools ◽  
Relative Coordinate

In quantum mechanics the hyper-spherical method is one of the most well-established and successful computational tools. The general theory of harmonic polynomials and hyper-spherical harmonics is of central importance in this paper. The interaction potential V is assumed to depend on the hyper-radius ρ only where ρ is the function of the Jacobi relative coordinate x1, x2,…, xn which are functions of the particles' relative positions.

On the error of approximations in quantum mechanics. I. General theory

1965 ◽  
Vol 257 (1081) ◽  
pp. 309-326 ◽  
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Computer Applications ◽  
Quantum Mechanical ◽  
Quantum Mechanical Calculations ◽  
Density Matrices ◽  
Single Error

General formulas for estimating the errors in quantum-mechanical calculations are given in the formalism of density matrices. Some properties of the traces of matrices are used to simplify the estimating and to indicate a way of obtaining a better approximation. It is shown that the simultaneous correction of all the equations to be fulfilled leads in most cases to a faster convergence than the exact fulfilment of some of the equations and approximating stepwise to some of the others. The corrective formulas contain only direct operations of the matrices occurring and so they are advantageous in computer applications. In the last section a ‘subjective error’ definition is given and by taking into account the weight of the errors of the several equations a faster convergence and a single error quantity is obtained. Some special applications of the method will be published later.

On the general theory of damping in quantum mechanics

1951 ◽  
Vol 8 (11) ◽  
pp. 817-842 ◽  
Author(s):  
M. Schönberg
Keyword(s):  
Quantum Mechanics ◽  
General Theory

scholarly journals Experiments on the symmetry of length and time

2021 ◽  
Author(s):  
Li Chunhong
Keyword(s):  
Experimental Data ◽  
Quantum Mechanics ◽  
General Theory ◽  
Piezoelectric Sensor ◽  
Atomic Scale ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Speed Of Light ◽  
Time Coordinate ◽  
Time Position

Abstract The F - t curve obtained from the process of applying and releasing force to the piezoelectric sensor shows that in the atomic scale, the time coordinate is equivalent to the position coordinate. The time-position coordinate relationship calculated by the experimental data is consistent with the geometric unit obtained in the general theory of relativity, thus the experiment verifies the symmetry of length and time,and connection between the microscopic - quantum mechanics and the macroscopic - general theory of relativity, and a new method for calculating the speed of light is obtained.

scholarly journals Redefining Gravity: Field versus Flow

2017 ◽  
Vol 9 (2) ◽  
pp. 87
Author(s):  
Mehmet Bora Cilek
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Alternative Theory ◽  
Curvature Effect ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Flow Mechanism ◽  
Spacetime Curvature ◽  
Field Versus ◽  
The Universe

General Theory of Relativity constitutes the framework for our understanding of the universe, with an emphasis on gravity. Many of Einstein’s predictions have been verified experimentally but General and Special Theories of Relativity contain several anomalies and paradoxes, yet to be answered. Also, there are serious conflicts with Quantum Mechanics; gravity being the weakest and least understood force, is a major problem.Supported by clear experimental evidence, it is theorised that gravity is not a field or spacetime curvature effect, but rather has a flow mechanism. This is not an alternative theory of gravity with an alternative metric. Established laws and equations from Newton and Einstein are essentially left unchanged. However, spacetime curvature is replaced with flow, producing a refined and compatible theory.

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