13,748 research outputs found
The energy level structure of a variety of one-dimensional confining potentials and the effects of a local singular perturbation
Motivated by current interest in quantum confinement potentials, especially
with respect to the Stark spectroscopy of new types of quantum wells, we
examine several novel one-dimensional singular oscillators. A Green function
method is applied, the construction of the necessary resolvents is reviewed and
several new ones are introduced. In addition, previous work on the singular
harmonic oscillator model, introduced by Avakian et al. is reproduced to verify
the method and results. A novel features is the determination of the spectra of
asymmetric hybrid linear and quadratic potentials. As in previous work, the
singular perturbations are modeled by delta functions.Comment: 14 pages, 10 figure
General Approach to Functional Forms for the Exponential Quadratic Operators in Coordinate-Momentum Space
In a recent paper [Nieto M M 1996 Quantum and Semiclassical Optics, 8 1061;
quant-ph/9605032], the one dimensional squeezed and harmonic oscillator
time-displacement operators were reordered in coordinate-momentum space. In
this paper, we give a general approach for reordering multi-dimensional
exponential quadratic operator(EQO) in coordinate-momentum space. An explicit
computational formula is provided and applied to the single mode and
double-mode EQO through the squeezed operator and the time displacement
operator of the harmonic oscillator.Comment: To appear in J. Phys. A: Mathematics and Genera
Functional Forms for the Squeeze and the Time-Displacement Operators
Using Baker-Campbell-Hausdorff relations, the squeeze and harmonic-oscillator
time-displacement operators are given in the form , where ,
, , and are explicitly determined. Applications are
discussed.Comment: 10 pages, LaTe
Complexified sigma model and duality
We show that the equations of motion associated with a complexified
sigma-model action do not admit manifest dual SO(n,n) symmetry. In the process
we discover new type of numbers which we called `complexoids' in order to
emphasize their close relation with both complex numbers and matroids. It turns
out that the complexoids allow to consider the analogue of the complexified
sigma-model action but with (1+1)-worldsheet metric, instead of
Euclidean-worldsheet metric. Our observations can be useful for further
developments of complexified quantum mechanics.Comment: 15 pages, Latex, improved versio
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