scholarly journals SOME CONSEQUENCES OF A GENERALIZATION TO HEISENBERG ALGEBRA IN QUANTUM ELECTRODYNAMICS

2003 ◽  
Vol 12 (09) ◽  
pp. 1687-1692 ◽  
Author(s):  
A. CAMACHO
Keyword(s):  
Uncertainty Principle ◽  
Quantum Electrodynamics ◽  
Uncertainty Relation ◽  
Heisenberg Algebra ◽  
Heisenberg Uncertainty Relation ◽  
Fundamental Part ◽  
Heisenberg Uncertainty

In this essay it will be shown that the introduction of a modification to Heisenberg algebra (here this feature means the existence of a minimal observable length), as a fundamental part of the quantization process of the electrodynamical field, renders states in which the uncertainties in the two quadrature components violate the usual Heisenberg uncertainty relation. Hence in this context it may be asserted that any physically realistic generalization of the uncertainty principle must include, not only a minimal observable length, but also a minimal observable momentum.

UNCERTAINTY PRINCIPLE, SQUEEZING, AND QUANTUM GROUPS

1992 ◽  
Vol 07 (40) ◽  
pp. 3759-3764 ◽  
Author(s):  
A.K. RAJAGOPAL ◽  
VIRENDRA GUPTA
Keyword(s):  
Quantum Mechanics ◽  
Coherent State ◽  
Quantum Groups ◽  
Uncertainty Principle ◽  
Unitary Transformation ◽  
Uncertainty Relation ◽  
Heisenberg Uncertainty Relation ◽  
Heisenberg Uncertainty ◽  
Complete Form

It is shown that the complete form of the Heisenberg Uncertainty Relation (HUR) must be employed in introducing the concepts of squeezing and coherent state in q-quantum mechanics. An important feature of this form of the HUR is that it is invariant under unitary transformation of the operators appearing in it and consequences of this are pointed out.

scholarly journals Mathematical Uncertainty Relations and their Generalization for Multiple Incompatible Observables

2017 ◽  
Vol 33 (1) ◽  
Author(s):  
Hung Quang Nguyen ◽  
Tu Quang Bui
Keyword(s):  
Uncertainty Principle ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Schwarz Inequality ◽  
Uncertainty Relations ◽  
Heisenberg Uncertainty Relation ◽  
Generalized Uncertainty Relation ◽  
Heisenberg Uncertainty ◽  
Incompatible Observables

We show that the famous Heisenberg uncertainty relation for two incompatible observables can be generalized elegantly to the determinant form for N arbitrary observables. To achieve this purpose, we propose a generalization of the Cauchy-Schwarz inequality for two sets of vectors. Simple consequences of the N-ary uncertainty relation are also discussed. Keywords: Generalized uncertainty relation, Generalized uncertainty principle, Generalized Cauchy-Schwarz inequality.

scholarly journals On the Semiclassical Approach of the Heisenberg Uncertainty Relation in the Strong Gravitational Field of Static Blackhole

2020 ◽  
Vol 22 (2) ◽  
pp. 15
Author(s):  
Fima Ardianto Putra
Keyword(s):  
Gravitational Field ◽  
Uncertainty Principle ◽  
Equivalence Principle ◽  
Uncertainty Relation ◽  
Fundamental Aspect ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty Relation ◽  
Strong Gravitational Field ◽  
Heisenberg Uncertainty ◽  
The Impact

Heisenberg Uncertainty and Equivalence Principle are the fundamental aspect respectively in Quantum Mechanic and General Relativity. Combination of these principles can be stated in the expression of Heisenberg uncertainty relation near the strong gravitational field i.e. pr   and Et  . While for the weak gravitational field, both relations revert to pr and Et. It means that globally, uncertanty principle does not invariant. This work also shows local stationary observation between two nearby points along the radial direction of blackhole. The result shows that the lower point has larger uncertainty limit than that of the upper point, i.e. . Hence locally, uncertainty principle does not invariant also. Through Equivalence Principle, we can see that gravitation can affect Heisenberg Uncertainty relation. This gives the impact to our’s viewpoint about quantum phenomena in the presence of gravitation. Key words: Heisenberg Uncertainty Principle , Equivalence Principle, and gravitational field 

Coherent and squeezed states for the 3D harmonic oscillator

2017 ◽  
Vol 31 (03) ◽  
pp. 1750019
Author(s):  
Amel Mazouz ◽  
Mustapha Bentaiba ◽  
Ali Mahieddine
Keyword(s):  
Harmonic Oscillator ◽  
Uncertainty Relation ◽  
Three Dimensional ◽  
Heisenberg Algebra ◽  
Squeezed States ◽  
Ladder Operators ◽  
Compression Effect ◽  
Precise Knowledge ◽  
Generalized Coherent States ◽  
Heisenberg Uncertainty

A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.

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