Hartmann potential with a minimal length and generalized recurrence relations for matrix elements

• URL: http://arxiv.org/abs/2002.03346v1
• Date: Sun, 9 Feb 2020 11:40:03 GMT
• Title: Hartmann potential with a minimal length and generalized recurrence relations for matrix elements
• Authors: Lamine Khodja, Mohamed Achour and Slimane Zaim
• Abstract summary: We study the Schr"odinger equation in the presence of the Hartmann potential with a generalized uncertainty principle. We pertubatively obtain the matrix elements of the hamiltonian at first order in the parameter deformation of $beta$ and show that some degenerate states are removed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work we study the Schr\"{o}dinger equation in the presence of the Hartmann potential with a generalized uncertainty principle. We pertubatively obtain the matrix elements of the hamiltonian at first order in the parameter of deformation $\beta$ and show that some degenerate states are removed. We give analytic expressions for the solutions of the diagonal matrix elements. Finally, we derive a generalized recurrence formula for the angular average values.

Related papers

• High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization [83.06112052443233]
  This paper studies kernel ridge regression in high dimensions under covariate shifts. By a bias-variance decomposition, we theoretically demonstrate that the re-weighting strategy allows for decreasing the variance. For bias, we analyze the regularization of the arbitrary or well-chosen scale, showing that the bias can behave very differently under different regularization scales.
  arXiv  Detail & Related papers  (2024-06-05T12:03:27Z)
• Entrywise error bounds for low-rank approximations of kernel matrices [55.524284152242096]
  We derive entrywise error bounds for low-rank approximations of kernel matrices obtained using the truncated eigen-decomposition. A key technical innovation is a delocalisation result for the eigenvectors of the kernel matrix corresponding to small eigenvalues. We validate our theory with an empirical study of a collection of synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2024-05-23T12:26:25Z)
• Supersymmetric Expansion Algorithm and complete analytical solution for the Hulthén and anharmonic potentials [0.0]
  An algorithm for providing analytical solutions to Schr"odinger's equation with non-exactly solvable potentials is elaborated. It represents a symbiosis between the logarithmic expansion method and the techniques of the superymmetric quantum mechanics.
  arXiv  Detail & Related papers  (2024-05-02T15:13:06Z)
• Three-Dimensional Eigenvalues of Harmonic Oscillator- and Coulomb-type Potentials from One-Dimensional Generalized Morse Potential: Perturbative Analyse based on Generalized Laguerre Polynomials [0.0]
  We present perturbative energy eigenvalues (up to second order) of Coulomb- and harmonic oscillator-type fields within a perturbation scheme. We have the required unperturbed eigenvalues ($E_n(0)$) analytically obtained by using similarities between the expressions obtained from unperturbed Hamiltonian(s) for two fields and obtained from the ones for one-dimensional generalized Morse field.
  arXiv  Detail & Related papers  (2023-11-14T05:30:33Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians [65.268245109828]
  We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations. We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix. A quantum algorithm to simulate the dynamics of the density matrix is proposed.
  arXiv  Detail & Related papers  (2023-06-14T23:08:51Z)
• $O(N^2)$ Universal Antisymmetry in Fermionic Neural Networks [107.86545461433616]
  We propose permutation-equivariant architectures, on which a determinant Slater is applied to induce antisymmetry. FermiNet is proved to have universal approximation capability with a single determinant, namely, it suffices to represent any antisymmetric function. We substitute the Slater with a pairwise antisymmetry construction, which is easy to implement and can reduce the computational cost to $O(N2)$.
  arXiv  Detail & Related papers  (2022-05-26T07:44:54Z)
• On symmetries of a matrix and its isospectral reduction [0.0]
  diagonalizable matrices in terms of their so-called isospectral reduction represent a versatile approach to the underlying eigenvalue problem. We show in the present work that it is possible to construct a corresponding symmetry of the original matrix.
  arXiv  Detail & Related papers  (2021-05-25T17:52:27Z)
• The truncated Coulomb potential revisited [0.0]
  We apply the Frobenius method to the Schr"odinger equation with a truncated Coulomb potential. By means of the tree-term recurrence relation for the expansion coefficients we truncate the series and obtain exact eigenfunctions and eigenvalues.
  arXiv  Detail & Related papers  (2020-08-04T19:20:21Z)
• The semiring of dichotomies and asymptotic relative submajorization [0.0]
  We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassen's theorem on preordered semirings. We find that an variant of relative submajorization, defined on unnormalized dichotomies, is characterized by real-valued monotones that are multiplicative under the tensor product and additive under the direct sum.
  arXiv  Detail & Related papers  (2020-04-22T14:13:26Z)
• Relative Error Bound Analysis for Nuclear Norm Regularized Matrix Completion [101.83262280224729]
  We develop a relative error bound for nuclear norm regularized matrix completion. We derive a relative upper bound for recovering the best low-rank approximation of the unknown matrix.
  arXiv  Detail & Related papers  (2015-04-26T13:12:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.