相关论文: Perturbative expansions in quantum mechanics
The $J$-matrix method is extended to difference and $q$-difference operators and is applied to several explicit differential, difference, $q$-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures…
We use quantum harmonic analysis for densely defined operators to provide a simplified proof of the Berger-Coburn theorem for boundedness of Toeplitz operators. In addition, we revisit compactness and Schatten-class membership of densely…
We give an explicit formula, as a formal differential operator, for quantum microformal morphisms of (super)manifolds that we introduced earlier. Such quantum microformal morphisms are essentially oscillatory integral operators or Fourier…
This is an update on the quasicentral modulus, an invariant for an n-tuple of Hilbert space operators and a rearrangement invariant norm, that plays a key-role in sharp multivariable generalizations of the classical Weyl-von Neumann-Kuroda…
This is the first part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using parameterized versions of splitting theorems in Morse theory we generalize some famous…
It is shown that for the one-dimensional anharmonic oscillator with potential $V(x)= a x^2 + b g x^3 +\ldots=\frac{1}{g^2}\,\hat{V}(gx)$, as well as for the radial oscillator $V(r)=\frac{1}{g^2}\,\hat{V}(gr)$ and for the perturbed Coulomb…
Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…
The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation…
Examples are given of non-Hermitian Hamiltonian operators which have a real spectrum. Some of the investigated operators are expressed in terms of the generators of the Weil-Heisenberg algebra. It is argued that the existence of an…
An iterative procedure perturbatively solving the quantum spectral curve of planar N=4 SYM for any operator in the sl(2) sector is presented. A Mathematica notebook executing this procedure is enclosed. The obtained results include 10-loop…
The problem of the characterization of all analytic potentials which give rise to isochronous oscillatory motions still open. However, there are several approaches to highlight motions with period $T(E) \equiv T_0$ independent on the…
The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have…
We study the 1/N expansion in noncommutative quantum mechanics for the anharmonic and Coulombian potentials. The expansion for the anharmonic oscillator presented good convergence properties, but for the Coulombian potential, we found a…
P\"oschl-Teller-driven solutions for quantum mechanical fluctuations are triggered off by single scalar field theories obtained through a systematic perturbative procedure for generating deformed defects. The analytical properties…
This work presented a perturbational decomposition method for simulating quantum evolution under the one-dimensional Ising model with both longitudinal and transverse fields. By treating the transverse field terms as perturbations in the…
The analytic and formal solutions to a family of singularly perturbed partial differential equations in the complex domain involving two complex time variables are considered. The analytic continuation properties of the solution of an…
We discuss the method of conformal mappings applied to perturbative QCD. The approach is based on the Borel-Laplace integral regulated with the principal value prescription and the expansion of the Borel transform in powers of the variable…
Starting on the basis of $q$-symmetric oscillator algebra and on the associate $q$-calculus properties, we study a deformed quantum mechanics defined in the framework of the basic square-integrable wave functions space. In this context, we…
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical…
We show that the all-orders WKB periods of one-dimensional quantum mechanical oscillators are governed by the refined holomorphic anomaly equations of topological string theory. We analyze in detail the double-well potential and the cubic…