scholarly journals Quantum Theory of Anharmonic Oscillators: Some Exact Relations between Matrix Elements and Their Use for Various Approximation Methods

1983 ◽  
Vol 70 (3) ◽  
pp. 629-646 ◽  
Author(s):  
K. Yamazaki
Keyword(s):  
Quantum Theory ◽  
Approximation Methods ◽  
Matrix Elements ◽  
Anharmonic Oscillators ◽  
Exact Relations

TIME-SYMMETRY AND IRREVERSIBILITY IN CHRONOTOPOLOGICAL QFT — APPLICATION TO THE CP- AND T-SYMMETRY VIOLATIONS

1999 ◽  
Vol 08 (06) ◽  
pp. 545-610
Author(s):  
C. SYROS
Keyword(s):  
Quantum Theory ◽  
Numerical Calculations ◽  
Matrix Elements ◽  
Temperature Dependent ◽  
Symmetry Violation ◽  
Unitary Evolution ◽  
Time Symmetry ◽  
Phase Angles ◽  
The Universe

A quantum logical alternative "Either non-measure preservation Or unitary evolution" exists in the framework of Schroedinger's theory. This explains irreversibility and allows to describe both time-symmetric and time-asymmetric processes in Hermitian quantum theory. The CPT and Noether's theorems remain valid in chronotopology. The Bohr-Einstein controversy, Wigner's conjecture and the Poincaré's non-recurrence are naturally explained. Extended numerical calculations correctly predict the CP- and T-symmetry violation coefficients |η2π0|, |ηπ±|, |ημ±|, |ηe±|, [Formula: see text] and their phase angles: arg (η)=ϕ2π0, ϕπ±, ϕμ±, ϕe± for the K0, [Formula: see text]-decays. A relationship is discovered between the mixing factor and the relevant matrix elements. The ratio "matter/antimatter" appears as temperature dependent in the Universe, antimatter decays prevailing at around T≥ 1024 Kelvin.

Quantum theory of anharmonic oscillators. II. Energy levels of oscillators with x2α anharmonicity

1976 ◽  
Vol 17 (7) ◽  
pp. 1320-1337 ◽  
Author(s):  
F. T. Hioe ◽  
Don MacMillen ◽  
E. W. Montroll
Keyword(s):  
Quantum Theory ◽  
Energy Levels ◽  
Anharmonic Oscillators

scholarly journals A Theory Of Errors in Quantum Measurement

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2439-2450
Author(s):  
S. G. Rajeev
Keyword(s):  
Quantum Theory ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Probability Distribution ◽  
Quantum Measurement ◽  
Probability Distributions ◽  
Matrix Elements ◽  
Random Errors ◽  
The Central Limit Theorem ◽  
The Matrix

It is common to model the random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an observable are distributed normally. We obtain the probability distribution this implies for the outcome of a measurement, exactly for the case of traceless 2 × 2 matrices and in the steepest descent approximation in general. Due to the phenomenon of 'level repulsion', the probability distributions obtained are quite different from the Gaussian.

scholarly journals Anharmonic oscillators in higher dimension: Accurate energy eigenvalues and matrix elements

Pramana ◽  
1989 ◽  
Vol 32 (6) ◽  
pp. 845-845
Author(s):  
V T A Bhargava ◽  
P M Mathews ◽  
M Seetharaman
Keyword(s):  
Higher Dimension ◽  
Matrix Elements ◽  
Anharmonic Oscillators ◽  
Energy Eigenvalues
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