Radial Uncertainty Product for Spherically Symmetric Potential in Position Space

• URL: http://arxiv.org/abs/2501.14831v1
• Date: Thu, 23 Jan 2025 07:50:33 GMT
• Title: Radial Uncertainty Product for Spherically Symmetric Potential in Position Space
• Authors: Avoy Jana,
• Abstract summary: The study derives the radial uncertainty relation analogous to the Cartesian form. The paper rigorously evaluates the normalized radial wave functions, expectation values, and uncertainties associated with both position and momentum.
• Score: 0.0
• License:
• Abstract: This paper presents a detailed analysis of the radial uncertainty product for quantum systems with spherically symmetric potentials. Using the principles of quantum mechanics, the study derives the radial uncertainty relation analogous to the Cartesian form and investigates its implications for three key spherically symmetric potentials: the Hydrogen atom, the infinite spherical potential well, and the spherical harmonic oscillator, all within the non-relativistic regime. Employing the Schrodinger equation in spherical coordinates, the paper rigorously evaluates the normalized radial wave functions, expectation values, and uncertainties associated with both position and momentum. Analytical derivations and numerical computations highlight the dependence of the uncertainty product on quantum numbers and system-specific parameters.

Related papers

• Generalized Radial Uncertainty Product for d-Dimensional Hydrogen Atom [0.0]
  This paper presents a comprehensive analysis of the generalized radial uncertainty product for the d-dimensional non-relativistic Hydrogen atom in position space. The results provide deeper insight into the role of dimensionality in quantum uncertainty relations and their implications for higher-dimensional quantum systems.
  arXiv  Detail & Related papers  (2025-02-05T19:26:34Z)
• Hilbert space geometry and quantum chaos [39.58317527488534]
  We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians. We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
  arXiv  Detail & Related papers  (2024-11-18T19:00:17Z)
• Noninvertible operators in one, two, and three dimensions via gauging spatially modulated symmetry [15.282090777675679]
  We construct concrete lattice models with non-invertible duality defects via gauging spatially modulated symmetries. Our work provides a unified and systematic analytical framework for constructing exotic duality defects by gauging relevant symmetries.
  arXiv  Detail & Related papers  (2024-09-25T08:52:07Z)
• Non-equilibrium quantum probing through linear response [41.94295877935867]
  We study the system's response to unitary perturbations, as well as non-unitary perturbations, affecting the properties of the environment. We show that linear response, combined with a quantum probing approach, can effectively provide valuable quantitative information about the perturbation and characteristics of the environment.
  arXiv  Detail & Related papers  (2023-06-14T13:31:23Z)
• Oscillation probabilities for a PT-symmetric non-Hermitian two-state system [0.0]
  There is growing interest in viable quantum theories with PT-symmetric non-Hermitian Hamiltonians. This Letter provides such a formulation, which relies crucially on the ability to span the state space in such a way as to the same positive-definite inner product.
  arXiv  Detail & Related papers  (2023-02-22T21:42:58Z)
• Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schr\"odinger equation with focusing saturable nonlinearity and PT-symmetric potential [13.844860643212105]
  We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schr"odinger (FNLS) equation. The continuous asymmetric soliton branch bifurcates from the fundamental symmetric one as the power exceeds some critical value. We explore the elastic/semi-elastic collision phenomena between symmetric and asymmetric solitons.
  arXiv  Detail & Related papers  (2022-10-01T13:18:22Z)
• SUSY-Nonrelativistic Quantum Eigenspectral Energy Analysis for Squared-Type Trigonometric Potentials Through Nikiforov-Uvarov Formalism [0.0]
  We presentExplicit and analytical bound-state solutions of the Schrodinger equation for squared-form trigonometric potentials within the framework of supersymmetric quantum mechanics (SUSYQM) It is remarkable to note that, when examined parametrically, they are of reliable and applicable forms concerning the mathematical treatment of various physical quantum systems prescribed in relativistic or nonrelativistic contexts.
  arXiv  Detail & Related papers  (2022-08-24T14:49:31Z)
• Machine Learning S-Wave Scattering Phase Shifts Bypassing the Radial Schr\"odinger Equation [77.34726150561087]
  We present a proof of concept machine learning model resting on a convolutional neural network capable to yield accurate scattering s-wave phase shifts. We discuss how the Hamiltonian can serve as a guiding principle in the construction of a physically-motivated descriptor.
  arXiv  Detail & Related papers  (2021-06-25T17:25:38Z)
• Multidimensional hydrogenic states: Position and momentum expectation values [0.0]
  The position and momentum probability densities of a multidimensional quantum system are fully characterized by means of the radial expectation values $langle ralpha rangle$ and $leftlangle palpha rightrangle$, respectively. These quantities have not been calculated in an analytical and effective manner up until now except for a number of three-dimensional hydrogenic states.
  arXiv  Detail & Related papers  (2020-11-24T17:34:14Z)
• Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
  We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
  arXiv  Detail & Related papers  (2020-11-06T19:00:07Z)
• Non-local divergence-free currents for the account of symmetries in two-dimensional wave scattering [0.0]
  We show that symmetry induced, non-local, divergence-free currents can be a useful tool for the description of the consequences of symmetries on wave scattering. We argue that the usual representation of the scattering wave function does not account for insufficient account for a proper description of the underlying potential symmetries.
  arXiv  Detail & Related papers  (2020-08-12T19:29:51Z)

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.