Relativistic Ladder Operators for the Three-Dimensional Harmonic Oscillator
نویسنده
چکیده
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 oscillator. Correspondence to the Schrödinger equation for the harmonic oscillator in the non-relativistic limit is demonstrated.
منابع مشابه
Supersymmetric Quantum Mechanics and Painlevé IV Equation
As it has been proven, the determination of general one-dimensional Schrödinger Hamiltonians having third-order differential ladder operators requires to solve the Painlevé IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a s...
متن کاملGeneralized Ladder Operators for Shape-invariant Potentials
A general form for ladder operators is used to construct a method to solve bound-state Schrödinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for ...
متن کاملCoulomb and quantum oscillator problems in conical spaces with arbitrary dimensions
The Schrödinger equations for the Coulomb and the Harmonic oscillator potentials are solved in the cosmic-string conical space-time. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic oscillator eigenfunctions is performed through the introduction of non-local ladder operators. By exploiting the hidden symmetry of the two-dimensional harmonic...
متن کاملN ov 2 00 1 Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions
The Schrödinger equations for the Coulomb and the Harmonic oscillator potentials are solved in the cosmic-string conical space-time. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic oscillator eigenfunctions is performed through the introduction of non-local ladder operators. By exploiting the hidden symmetry of the two-dimensional harmonic...
متن کاملFactorization, Ladder Operators and Isospectral Structures
Using the modified factorization method employed by Mielnik for the harmonic oscillator, we show that isospectral structures associated with a second order operator H, can always be constructed whenever H could be factored, or exist ladder operators for its eigenfunctions. Three examples are shown, and properties like completeness and integrability are discused for the general case.
متن کامل