scholarly journals Refinement of Robertson-type uncertainty principles with geometric interpretation

2016 ◽  
Vol 14 (02) ◽  
pp. 1650013 ◽  
Author(s):  
Attila Lovas ◽  
Attila Andai
Keyword(s):  
Geometric Interpretation ◽  
Covariance Matrices ◽  
Quantum Mechanical ◽  
Uncertainty Principles ◽  
Quantum Covariance ◽  
Usual Quantum

A generalization of the classical covariance for quantum mechanical observables has previously been presented by Gibilisco et al. Gibilisco and Isola has proved that the usual quantum covariance gives the sharpest inequalities for the determinants of covariance matrices. We introduce a new generalization of the classical covariance which gives better inequalities than the classical one, furthermore it has a direct geometric interpretation.

scholarly journals AN ENTROPIC PICTURE OF EMERGENT QUANTUM MECHANICS

2012 ◽  
Vol 09 (05) ◽  
pp. 1250048 ◽  
Author(s):  
D. ACOSTA ◽  
P. FERNÁNDEZ DE CÓRDOBA ◽  
J. M. ISIDRO ◽  
J. L. G. SANTANDER
Keyword(s):  
Quantum Mechanics ◽  
Quantum Mechanical ◽  
Entropy Flow ◽  
Planck’S Constant ◽  
Formal Derivation ◽  
Usual Quantum ◽  
Holographic Screen ◽  
Holographic Screens ◽  
Planck's Constant ◽  
Emergent Quantum Mechanics

Quantum mechanics emerges à la Verlinde from a foliation of ℝ3 by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantized in units of Boltzmann's constant kB. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on ℝ3. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant ℏ from Boltzmann's constant kB.

scholarly journals Nonlinear Generalisation of Quantum Mechanics

2021 ◽  
Author(s):  
Alireza Jamali
Keyword(s):  
Quantum Mechanics ◽  
Quantum Mechanical ◽  
Uncertainty Principles ◽  
General Validity ◽  
Klein Gordon ◽  
Mechanical Momentum

A new definition for quantum-mechanical momentum is proposed which yields novel nonlinear generalisations of Schrödinger and Klein-Gordon equations. It is thence argued that the superposition and uncertainty principles as they stand cannot have general validity.

EFFECT OF MAXIMUM MOMENTUM ON QUANTUM MECHANICAL SCATTERING AND BOUND STATES

2013 ◽  
Vol 28 (15) ◽  
pp. 1350061 ◽  
Author(s):  
CHEE-LEONG CHING ◽  
RAJESH R. PARWANI
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Quantum Mechanical ◽  
Position Uncertainty ◽  
Exact Position ◽  
Usual Quantum ◽  
Quantum Mechanical Scattering ◽  
Mechanical Scattering

We construct the exact position representation for a deformed (non-relativistic) quantum mechanics which exhibits an intrinsic maximum momentum and use it to study problems such as a particle in a box and an asymmetric well. In particular, we show that unlike usual quantum mechanics, the present deformed case delays the formation of bound states in a finite potential well, a distinguishing feature that might be relevant for empirical investigations. We also contrast our results with the string-motivated type of deformed quantum mechanics which incorporates a minimum position uncertainty rather than a maximum momentum.

On the quantum mechanical solutions with minimal length uncertainty

2016 ◽  
Vol 31 (18) ◽  
pp. 1650101 ◽  
Author(s):  
Homa Shababi ◽  
Pouria Pedram ◽  
Won Sang Chung
Keyword(s):  
Heat Capacity ◽  
Partition Function ◽  
Harmonic Oscillator ◽  
Internal Energy ◽  
Free Particle ◽  
Minimal Length ◽  
Quantum Mechanical ◽  
Uncertainty Principles ◽  
Trigonometric Functions ◽  
Eigenvalues And Eigenfunctions

In this paper, we study two generalized uncertainty principles (GUPs) including [Formula: see text] and [Formula: see text] which imply minimal measurable lengths. Using two momentum representations, for the former GUP, we find eigenvalues and eigenfunctions of the free particle and the harmonic oscillator in terms of generalized trigonometric functions. Also, for the latter GUP, we obtain quantum mechanical solutions of a particle in a box and harmonic oscillator. Finally we investigate the statistical properties of the harmonic oscillator including partition function, internal energy, and heat capacity in the context of the first GUP.

scholarly journals Tunneling Quantum Dynamics in Ammonia

2021 ◽  
Vol 22 (15) ◽  
pp. 8282
Author(s):  
Ciann-Dong Yang ◽  
Shiang-Yi Han
Keyword(s):  
Nitrogen Atom ◽  
Quantum Dynamics ◽  
Equations Of Motion ◽  
Quantum Probability ◽  
Quantum Mechanical ◽  
Quantum Trajectories ◽  
Experimental Measurements ◽  
Hamilton Equations ◽  
Usual Quantum ◽  
Tunneling Phenomenon

Ammonia is a well-known example of a two-state system and must be described in quantum-mechanical terms. In this article, we will explain the tunneling phenomenon that occurs in ammonia molecules from the perspective of trajectory-based quantum dynamics, rather than the usual quantum probability perspective. The tunneling of the nitrogen atom through the potential barrier in ammonia is not merely a probability problem; there are underlying reasons and mechanisms explaining why and how the tunneling in ammonia can happen. Under the framework of quantum Hamilton mechanics, the tunneling motion of the nitrogen atom in ammonia can be described deterministically in terms of the quantum trajectories of the nitrogen atom and the quantum forces applied. The vibrations of the nitrogen atom about its two equilibrium positions are analyzed in terms of its quantum trajectories, which are solved from the Hamilton equations of motion. The vibration periods are then computed by the quantum trajectories and compared with the experimental measurements.

scholarly journals Nonlinear Generalisation of Quantum Mechanics

2021 ◽  
Author(s):  
Alireza Jamali
Keyword(s):  
Quantum Mechanics ◽  
Quantum Mechanical ◽  
Uncertainty Principles ◽  
General Validity ◽  
Klein Gordon ◽  
Mechanical Momentum

A new definition for quantum-mechanical momentum is proposed which yields novel nonlinear generalisations of Schrödinger and Klein-Gordon equations. It is thence argued that the superposition and uncertainty principles as they stand cannot have general validity.

Mathematical simulation of error functions of decision-making at tolerance control of measuring techniques availability

Metrologiya ◽  
2020 ◽  
pp. 3-15
Author(s):  
Rustam Z. Khayrullin ◽  
Alexey S. Kornev ◽  
Andrew A. Kostoglotov ◽  
Sergey V. Lazarenko
Keyword(s):  
Measurement Error ◽  
Geometric Interpretation ◽  
Measuring Instruments ◽  
Measured Quantity ◽  
Metrological Examination ◽  
Technical Documentation ◽  
Error Functions ◽  
Measuring Techniques ◽  
Tolerance Control ◽  
Laws Of Distribution

Analytical and computer models of false failure and undetected failure (error functions) were developed with tolerance control of the parameters of the components of the measuring technique. A geometric interpretation of the error functions as two-dimensional surfaces is given, which depend on the tolerance on the controlled parameter and the measurement error. The developed models are applicable both to theoretical laws of distribution, and to arbitrary laws of distribution of the measured quantity and measurement error. The results can be used in the development of metrological support of measuring equipment, the verification of measuring instruments, the metrological examination of technical documentation and the certification of measurement methods.

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