Semiclassical states for critical Choquard equations
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Semiclassical physics
Riesz potential
Semiclassical physics
Riesz potential
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In this article we study the semiclassical spectral measures associated with Schrödinger operators on $R^n$. In particular we compute the first few coefficients of the asymptotic expansions of these measures and, as an application, give an alternative proof of Colin de Verdiere's result on recovering one dimensional potential wells from semiclassical spectral data. We also study the relation of semiclassical spectra measures to Birkhoff normal forms and describe a generalization of the asymptotic expansion above to the Schrödinger operator in the presence of a magnetic field.
Semiclassical physics
Schrödinger's cat
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The chemical potiential for the ground states of the atomic elements have been calculated within the semiclassical approximation The present work closely follows Schwinger and Englert's semiclassical treatment of atomic structure.
Semiclassical physics
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In this paper, we develop a semiclassical calculus on compact nil-manifolds. As an application of the former, we obtain asymptotics such as generalised Weyl laws for positive Rockland operators on any graded compact nil-manifolds. We also define and study semiclassical limits and quantum limits in this context.
Semiclassical physics
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Tunneling in the one-dimensional Eckart system is treated by a semiclassical method that describes the S-matrix in terms of an integral over the initial momenta of real-valued classical trajectories. The results are found to be sensitive to a certain parameter γ which is expected to be essentially arbitrary for classically allowed processes. Analysis of the semiclassical error allows formulation of conditions for the validity of the tunneling treatment. This, in turn, leads to an explanation for the sensitivity of the results to γ and an understanding of how this parameter should be chosen. With an optimized choice, the semiclassical method is found to yield very accurate tunneling results even for probabilities as small as 10−10. The relationship between the present method and the conventional uniform semiclassical treatment of barrier tunneling is discussed.
Semiclassical physics
Matrix (chemical analysis)
Representation
Value (mathematics)
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Semiclassical physics
Saddle point
Matrix (chemical analysis)
Saddle
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Arnol'd showed that simple semiclassical methods applied to potentials with discrete symmetries yield 'quasimodes' which do not have the same degeneracy properties as true eigenstates; here it is shown that the true semiclassical states are simple linear combinations of the quasimodes.
Semiclassical physics
Degeneracy (biology)
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The chemical potiential for the ground states of the atomic elements have been calculated within the semiclassical approximation The present work closely follows Schwinger and Englert's semiclassical treatment of atomic structure.
Semiclassical physics
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Semiclassical physics
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Semiclassical wave functions of bound states are constructed for an integrable model having R(4) ≃SU(2)⊗SU(2) symmetry. Each eigenstate is expressed as an integral of generalized coherent states over a quantized torus, which satisfies a standard Einstein-Brillouin-Keller quantization condition. Obtained wave functions as well as transition rates are compared with those of exact solutions calculated via diagonalization. Semiclassical and exact results show a close correspondence over a broad range of the parameters in the model.
Semiclassical physics
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