%0 Journal Article %1 WOS:000388154600004 %A Aguiar, V %A Nascimento, J P G %A Guedes, I %C RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS %D 2016 %I ELSEVIER %J INTERNATIONAL JOURNAL OF MASS SPECTROMETRY %K Hamiltonian; Lewis Riesenfeld Time-dependent Uncertainty and method} relations; trap; {Penning %P 21-28 %R 10.1016/j.ijms.2016.09.007 %T Exact wave functions and uncertainties for a spinless charged particle in a time-dependent Penning trap %V 409 %X We use the dynamical invariant method and two unitary transformations to obtain the exact Schrodinger wave functions, psi(nmk), (r, t), for a spinless charged particle in a time-dependent Penning trap. For the special case n = m = k = 0, we obtain the analytical expressions for the uncertainties in terms of two c-number functions satisfying a Milne-Pinney-like equation. We analyze the static and the time dependent cases. For the former, where B (t) = B(0)k and V (t) = V-0, we observe that the Heisenberg and Robertson-Schrodinger uncertainty relations are fulfilled and the behavior of the uncertainties Delta x, y and Delta p(x), p(y), when B-0 changes indicates the occurrence of a squeezing phenomenon. For the later, where B (t) = (B-0(2) + B'cos(2) (vt))(1/2)k andV (t) = V-0 + V'Cos(2) (vt), we observe that Delta x, y oscillate in time exhibiting a squeezing phenomenon. Relations among the uncertainties, Shannon entropies and Fisher lengths were stablished. We observe for both cases that the Shannon entropy in position, S-r, and in momentum, S-p, satisfy the relation S-r + S-p >= 3 (1 + ln pi), while the Fisher lengths delta r and delta p exhibit a lower bound than the uncertainties Delta r, p. (C) 2016 Elsevier B.V. All rights reserved.

@article{WOS:000388154600004, abstract = {We use the dynamical invariant method and two unitary transformations to obtain the exact Schrodinger wave functions, psi(nmk), (r, t), for a spinless charged particle in a time-dependent Penning trap. For the special case n = m = k = 0, we obtain the analytical expressions for the uncertainties in terms of two c-number functions satisfying a Milne-Pinney-like equation. We analyze the static and the time dependent cases. For the former, where B (t) = B(0)k and V (t) = V-0, we observe that the Heisenberg and Robertson-Schrodinger uncertainty relations are fulfilled and the behavior of the uncertainties Delta x, y and Delta p(x), p(y), when B-0 changes indicates the occurrence of a squeezing phenomenon. For the later, where B (t) = (B-0(2) + B'cos(2) (vt))(1/2)k andV (t) = V-0 + V'Cos(2) (vt), we observe that Delta x, y oscillate in time exhibiting a squeezing phenomenon. Relations among the uncertainties, Shannon entropies and Fisher lengths were stablished. We observe for both cases that the Shannon entropy in position, S-r, and in momentum, S-p, satisfy the relation S-r + S-p >= 3 (1 + ln pi), while the Fisher lengths delta r and delta p exhibit a lower bound than the uncertainties Delta r, p. (C) 2016 Elsevier B.V. All rights reserved.}, added-at = {2022-05-23T20:00:14.000+0200}, address = {RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS}, author = {Aguiar, V and Nascimento, J P G and Guedes, I}, biburl = {https://www.bibsonomy.org/bibtex/25a41c7b3f5a068359c59ac414b600307/ppgfis_ufc_br}, doi = {10.1016/j.ijms.2016.09.007}, interhash = {7f1c49bb345f2e4adcb0ba643913b51c}, intrahash = {5a41c7b3f5a068359c59ac414b600307}, issn = {1387-3806}, journal = {INTERNATIONAL JOURNAL OF MASS SPECTROMETRY}, keywords = {Hamiltonian; Lewis Riesenfeld Time-dependent Uncertainty and method} relations; trap; {Penning}, pages = {21-28}, publisher = {ELSEVIER}, pubstate = {published}, timestamp = {2022-05-23T20:00:14.000+0200}, title = {Exact wave functions and uncertainties for a spinless charged particle in a time-dependent Penning trap}, tppubtype = {article}, volume = 409, year = 2016 }