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Coupled harmonic oscillator systems: An elementary algebraic decoupling approach

Tova Feldmann, M. Cohen, B. L. Burrows

We present simple explicit coordinate transformations which serve to decouple the Schrödinger equation for a pair of (not necessarily identical) harmonic oscillators in the presence of bilinear perturbing potentials. We derive general conditions for the decoupling, and give some examples of physical interest. These include the much studied example with just a static perturbation, the parallel problem with a dynamic coupling term, and the classic example of an isotropic two-dimensional oscillator in a transverse magnetic field, first solved by Fock (1928) by separation of variables.We present simple explicit coordinate transformations which serve to decouple the Schrödinger equation for a pair of (not necessarily identical) harmonic oscillators in the presence of bilinear perturbing potentials. We derive general conditions for the decoupling, and give some examples of physical interest. These include the much studied example with just a static perturbation, the parallel problem with a dynamic coupling term, and the classic example of an isotropic two-dimensional oscillator in a transverse magnetic field, first solved by Fock (1928) by separation of variables.

Journal of Mathematical PhysicsSep 1, 20004 citations

Quantum Oscillators: General Considerations

Elsevier eBooksJan 1, 19950 citations

Mass effects in a Three-Body System Bound by Harmonic Oscilators

A.C.B. Antunes, L. J. Antunes

The problem of three different masses bound by harmonic oscillator potentials is solved exactly. It is shown that Jacobi coordinates cannot, in general, decouple this system into two three-dimensional oscillators but this decoupling can always be obtained in terms of the normal coordinates. The condition for the decoupling in Jacobi coordinates is given. It is shown that the mean distance between each pair of particles depends upon their masses.

arXiv:hep-ph/9608377Aug 20, 19960 citations

Treating Many-Body Quantum Systems by Means of Classical Mechanics

Andrey R. Kolovsky

Springer proceedings in physicsJan 1, 20173 citations

Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics

Edwin Langmann A, Ari Arievich Laptev, Cornelius Paufler

We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the harmonic oscillator or the free particle on the circle. The generalization of these examples to the many-body case yields quantum models of distinguishable and interacting particles in one dimensions which can be solved explicitly and by simple means. Our considerations lead us to a simple method to construct exactly solvable quantum many-body systems of Calogero-Sutherland type. 1. Introduction. In this paper we define and study peculiar self-adjoint extensions of simple differential operators like the one defining the quantum mechanical harmonic oscillator. We also find the explicit solution of some of the resulting quantum mechanical models and discuss their physical interpretations. These examples provide amusing illustrations that theWe study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the harmonic oscillator or the free particle on the circle. The generalization of these examples to the many-body case yields quantum models of distinguishable and interacting particles in one dimensions which can be solved explicitly and by simple means. Our considerations lead us to a simple method to construct exactly solvable quantum many-body systems of Calogero-Sutherland type. 1. Introduction. In this paper we define and study peculiar self-adjoint extensions of simple differential operators like the one defining the quantum mechanical harmonic oscillator. We also find the explicit solution of some of the resulting quantum mechanical models and discuss their physical interpretations. These examples provide amusing illustrations that the

Jan 1, 20054 citations

The Quantum Mechanical Harmonic Oscillator

Erich W. Schmid, Gerhard Spitz, Wolfgang Lösch

Springer eBooksJan 1, 19880 citations

Mapping quantum many-body system to decoupled harmonic oscillators: General discussions and examples

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Mapping quantum many-body system to decoupled harmonic oscillators: General discussions and examples

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