Volume 42, Issue 4
April 1994, pages 285-374
pp 285-297 April 1994
Non perturbative effective potentials of quantum oscillators
Non perturbative analogues of the Gaussian effective potential (GEP) are defined for quantum oscillators obeyingq—or (q,p)—deformed commutation relations. These are called the non perturbativeq-effective potential (NP_{q}EP) and the non perturbativeqp effective potential (NP_{qp} EP), in the respective cases. A system-specific effective potential (SSEP) is also introduced by means of an additional minimization with respect to theq orq andp parameters. The method is applied toq and (q,p) oscillators of the quartic and sextic types. The SSEP in the case of ground states of theq-oscillators corresponds toq=1, which is the ordinary bosonic limit. A potential shape transition that involves the conversion of a double well to a single well or vice versa, is seen to exist in the case of quantum oscillators sitting in a double well potential.
pp 299-309 April 1994
Coherent states and squeezed states of realq-deformed quantum oscillators
G Vinod K Babu Joseph V C Kuriakose
A detailed physical characterisation of the coherent states and squeezed states of a realq-deformed oscillator is attempted. The squeezing andq-squeezing behaviours are illustrated by three different model Hamiltonians, namely i) Batemann Hamiltonian ii) harmonic oscillator with time dependent mass and frequency and iii) a system with constant mass and time-dependent frequency.
pp 311-314 April 1994
Squeezed vacuum as an eigenstate of two-photon annihilation operator
C L Mehta Anil K Roy G M Saxena
We introduce the inverse annihilation and creation operatorsâ^{−1} andâ^{+-1} by their actions on the number states. We show that the squeezed vacuum exp(1/2;ξâ^{+2}]|0> and squeezed first number state exp[1/2;ξâ^{+2}]|n=1> are respectively the eigenstates of the operators (â^{†−1}â) and (ââ^{+-1}) with the eigenvalue ξ.
pp 315-318 April 1994
A note on the harmonic plus inverse-harmonic potential in quantum mechanics
The ground state of a class of potentials described byV(x)=a_{20}x^{2}+a_{1}/x^{2} is investigated. This potential possesses some distinct features like that of a symmetric double-well potential, and can be used in modelling the fusion process of two identical nuclei as well.
pp 319-332 April 1994
WKB approximation in complex time II
The non-perturbative method, developed recently, of WKB approximation in complex time is applied to some known curved space time. Three cases namely (1) static in and out region, (2) non-static in and out region, (3) static in and non static out region are considered here. We find non-trivial particle production corresponding to the quantum vacuum definition of Castagnino and Mazzitelli.
pp 333-340 April 1994
The Schrödinger equation with the potentialV(r)=D[exp(−2β(r−r_{e}))−2exp(−β(r−r_{e}))] is treated in the framework of the hypervirial-renormalization parameter scheme. The energy eigenvalues of various eigenstates for different molecules are calculated.
pp 341-348 April 1994
Ensemble interpretation of the EPR-Bell correlations
The EPR-Bell correlations between the spins of a pair of particles originally in a singlet state are discussed both on the basis of the mathematical formalism of quantum mechanics and the ensemble interpretation. It is shown that the correlations predicted by the mathematical formalism are in agreement with those expected on the basis of the ensemble interpretation, if the electrons are treated as distinguishable particles after they separate and undergo observation. In this case, the correlations are only in partial agreement with agedanken experiment of Mermin on the subject. It is pointed out, however, that agreement with Mermin’s conclusions is possible if one treats the electrons as indistinguishable even when they are subjected to observation after separation, though there is no obvious theoretical justification for doing so.
pp 349-363 April 1994
Analysis of the excitation functions of (α, xnyp) reactions on natural copper
N L Singh B J Patel D R S Somayajulu S N Chintalapudi
Excitation functions of the reactions^{63}Cu[(α, n), (α, 2n)+(α, pn)] and^{65}Cu[(α, n), (α, 2n), (α, 3n), (α, 4n)+(α, p3n)] were investigated up to 50 MeV using stacked foil activation technique and Ge(Li) gamma ray spectroscopy method. Since natural copper used as the target has two odd-mass stable isotopes of abundance,^{63}Cu(69.17%) and^{65}Cu(30.83%), their activation in some cases, gives the same residual nucleus through different reaction channels but with very different threshold energies. In such cases, the individual reaction cross sections are separated with the ratio of theoretical cross sections. The experimental results were compared with the predictions of preequilibrium hybrid model of Blann. A general agreement was found in all reactions using initial exciton numbern_{0}=4(4p0h) and also preequilibrium fraction depends on the incident particle energy.
pp 365-374 April 1994
Multiple scattering of gamma rays in water, concrete and sand
G S Bhandal Vijay Kumar Rama Rani K A Waldeep K Singh
The transmitted photon spectra of^{133}Ba,^{22}Na,^{137}Cs,^{54}Mn and^{60}Co point sources are measured through different thicknesses of water, concrete and sand. The multiple-scatter peaks observed in these materials at 60, 90 and 100 keV energies respectively are found to be independent of incident photon energy and thickness of the medium.
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