The paper obtains an explicit analytic expression for the radial position-momentum uncertainty product of the d-dimensional hydrogen atom in terms of the quantum numbers n and ℓ and the dimension d.
Radial Uncertainty Product for Spherically Symmetric Potential in Position Space
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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.
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Generalized Radial Uncertainty Product for d-Dimensional Hydrogen Atom
The paper obtains an explicit analytic expression for the radial position-momentum uncertainty product of the d-dimensional hydrogen atom in terms of the quantum numbers n and ℓ and the dimension d.