Ladder Operators for the Spherical 3D Harmonic Oscillator

Relativistic Ladder Operators for the Three-Dimensional Harmonic Oscillator

The quantum constraint equations for a relativistic three-dimensional harmonic oscillator are shown to find concise expression in terms of Lorentz covariant ladder operators. These ladder operators consist of two conjugate 4-vectors that are each constrained to generate three linearly independent combinations of ladder operator components for raising and lowering the eigenstates of the oscillat...

Eigenvalue Problem for Schrödinger Operators and Time-Dependent Harmonic Oscillator

It is shown that the eigenvalue problem for the Hamiltonians of the standard form, H = p/(2m) + V (x), is equivalent to the classical dynamical equation for certain harmonic oscillators with time-dependent frequency. This is another indication of the central role played by time-dependent harmonic oscillators in quantum mechanics. The utility of the known results for eigenvalue problem in the so...

3D Objects Indexing Using Spherical Harmonic for Optimum Measurement Similarity

Abstract—In this paper, we propose a method for threedimensional (3-D)-model indexing based on defining a new descriptor, which we call new descriptor using spherical harmonics. The purpose of the method is to minimize, the processing time on the database of objects models and the searching time of similar objects to request object. Firstly we start by defining the new descriptor using a new di...

Robust Designs for 3d Shape Analysis with Spherical Harmonic Descriptors

Spherical harmonic descriptors are frequently used for describing threedimensional shapes in terms of Fourier coefficients corresponding to an expansion of a function defined on the unit sphere. In a recent paper Dette, Melas and Pepelysheff (2005) determined optimal designs with respect to Kiefer’s Φp-criteria for regression models derived from a truncated Fourier series. In particular it was ...

Harmonic Oscillator