scholarly journals The uncertainty relations and minimum uncertainty states

2003 ◽  
Vol 52 (12) ◽  
pp. 2961
Author(s):  
Deng Wen-Ji ◽  
Xu Yun-Hua ◽  
Liu Ping
2014 ◽  
Vol 3 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Piero Chiarelli

This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle is fully compatible with the postulate of finite transmission speed of light and information. The theory shows that the measurement process performed in the large scale classical limit in presence of background noise, cannot have a duration smaller than the time need to the light to travel the distance up to which the quantum non-local interaction extend itself. The product of the minimum measuring time multiplied by the variance of energy fluctuation due to presence of stochastic noise shows to lead to the minimum uncertainty principle. The paper also shows that the uncertainty relations can be also derived if applied to the indetermination of position and momentum of a particle of mass m in a quantum fluctuating environment.


2019 ◽  
Vol 383 (16) ◽  
pp. 1850-1855
Author(s):  
Anindita Bera ◽  
Debmalya Das ◽  
Aditi Sen(De) ◽  
Ujjwal Sen

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1851-1859 ◽  
Author(s):  
JOSÉ RÉCAMIER ◽  
W. LUIS MOCHÁN ◽  
MARÍA GORAYEB ◽  
JOSÉ L. PAZ ◽  
ROCÍO JÁUREGUI

We construct a deformed oscillator whose energy spectra is similar to that of a Morse potential. We obtain a convenient algebraic representation of the displacement and the momentum of a Morse oscillator by expanding them in terms of deformed creation and annihilation operators and we compute their average values between approximate coherent states of the deformed oscillator, and we compare them to the results obtained using the exact Morse coordinate and momenta. Finally we evaluate the temporal evolution of the dispersion (Δx)(Δp) and show that these states are not minimum uncertainty states.


1996 ◽  
Vol 13 (7) ◽  
pp. 1407
Author(s):  
Darryl J. Sanchez ◽  
Robert W. Conley ◽  
J. K. McIver

Author(s):  
Norman J. Morgenstern Horing

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.


Author(s):  
Seeta Vasudevrao ◽  
I. Reena ◽  
A. R. Usha Devi ◽  
Sudha ◽  
A. K. Rajagopal

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Stephan Sponar ◽  
Armin Danner ◽  
Vito Pecile ◽  
Nico Einsidler ◽  
Bülent Demirel ◽  
...  

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