scholarly journals Ladder Operators for Lamé Spheroconal Harmonic Polynomials

2012 ◽  
Author(s):  
Ricardo Méndez-Fragoso
Keyword(s):  
Harmonic Polynomials ◽  
Ladder Operators

HYPER-SPHERICAL HARMONICS AND ANHARMONICS IN m-DIMENSIONAL SPACE

2008 ◽  
Vol 17 (06) ◽  
pp. 1125-1130
Author(s):  
M. R. SHOJAEI ◽  
A. A. RAJABI ◽  
H. HASANABADI
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Spherical Harmonics ◽  
Interaction Potential ◽  
Dimensional Space ◽  
Harmonic Polynomials ◽  
Central Importance ◽  
Computational Tools ◽  
Relative Coordinate

In quantum mechanics the hyper-spherical method is one of the most well-established and successful computational tools. The general theory of harmonic polynomials and hyper-spherical harmonics is of central importance in this paper. The interaction potential V is assumed to depend on the hyper-radius ρ only where ρ is the function of the Jacobi relative coordinate x1, x2,…, xn which are functions of the particles' relative positions.

scholarly journals Hermite Functions and Fourier Series

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 853
Author(s):  
Enrico Celeghini ◽  
Manuel Gadella ◽  
Mariano del Olmo
Keyword(s):  
Fourier Transform ◽  
Hermite Functions ◽  
Quantum Oscillator ◽  
Linear Combinations ◽  
Ladder Operators ◽  
Orthonormal Bases ◽  
Integrable Functions ◽  
The Fourier Transform ◽  
The One ◽  
Square Integrable Functions

Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle (L2(C)) and in l2(Z), which are related to each other by means of the Fourier transform and the discrete Fourier transform. These relations are unitary. The construction of orthonormal bases requires the use of the Gramm–Schmidt method. On both spaces, we have provided ladder operators with the same properties as the ladder operators for the one-dimensional quantum oscillator. These operators are linear combinations of some multiplication- and differentiation-like operators that, when applied to periodic functions, preserve periodicity. Finally, we have constructed riggings for both L2(C) and l2(Z), so that all the mentioned operators are continuous.

Regular solids and harmonic polynomials

1945 ◽  
Vol 12 (4) ◽  
pp. 629-644 ◽  
Author(s):  
E. F. Beckenbach ◽  
Maxwell Reade
Keyword(s):  
Harmonic Polynomials

Algebraic structure of Dirac–Pauli equation with account to AMM of neutron in the presence of magnetic field with cylindrical symmetry

2021 ◽  
pp. 2150121
Author(s):  
Masoud Seidi
Keyword(s):  
Magnetic Field ◽  
Lie Algebra ◽  
Algebraic Structure ◽  
Anomalous Magnetic Moment ◽  
Casimir Operator ◽  
Cylindrical Symmetry ◽  
Pauli Equation ◽  
Eigenvalues And Eigenfunctions ◽  
Ladder Operators ◽  
Nu Method

The eigenvalues and eigenfunctions of Dirac–Pauli equation have been obtained for a neutron with anomalous magnetic moment (AMM) in the presence of a strong magnetic field with cylindrical symmetry. In our calculations, the Nikiforov and Uvarov (NU) method has been used. Using the eigenfunctions and construction of the ladder operators, we show that these generators satisfy su(2) Lie algebra and computed the second-order Casimir operator of the lie algebra.

scholarly journals A demonstration that electroweak theory can violate parity automatically (leptonic case)

2018 ◽  
Vol 33 (04) ◽  
pp. 1830005 ◽  
Author(s):  
C. Furey
Keyword(s):  
Clifford Algebra ◽  
Ad Hoc ◽  
Higgs Bosons ◽  
Electroweak Theory ◽  
Ladder Operators ◽  
Raising And Lowering Operators ◽  
Ladder Operator ◽  
Left And Right ◽  
Electroweak Model ◽  
Lowering Operators

We bring to light an electroweak model which has been reappearing in the literature under various guises.[Formula: see text] In this model, weak isospin is shown to act automatically on states of only a single chirality (left). This is achieved by building the model exclusively from the raising and lowering operators of the Clifford algebra [Formula: see text]. That is, states constructed from these ladder operators mimic the behaviour of left- and right-handed electrons and neutrinos under unitary ladder operator symmetry. This ladder operator symmetry is found to be generated uniquely by [Formula: see text] and [Formula: see text]. Crucially, the model demonstrates how parity can be maximally violated, without the usual step of introducing extra gauge and extra Higgs bosons, or ad hoc projectors.

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