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On Bound Electron Pairs on the Half-Line

Joachim Kerner

arXiv:1708.03753Reports on Mathematical PhysicsMar 1, 20197 citations

Two-particle bound states on a lattice

P. E. Kornilovitch

arXiv:2305.02548Annals of PhysicsDec 14, 20239 citations

On a non-separable quantum many-particle system on the half-line

Joachim Kerner, Tobias Mühlenbruch

In this paper we will report on a one-dimensional, non-separable quantum many-particle system.It consists of two (distinguishable) particles moving on the half-line R + being subjected to two different kinds of two-particle interactions: singular many-particle interactions localized at the origin and a binding-potential leading to a molecular-like state.We will formulate the model precisely, obtaining a well-defined self-adjoint operator (the Hamiltonian for our system) and elaborate on its spectral properties.In addition, we will present possible directions for future research.In this paper we will report on a one-dimensional, non-separable quantum many-particle system.It consists of two (distinguishable) particles moving on the half-line R + being subjected to two different kinds of two-particle interactions: singular many-particle interactions localized at the origin and a binding-potential leading to a molecular-like state.We will formulate the model precisely, obtaining a well-defined self-adjoint operator (the Hamiltonian for our system) and elaborate on its spectral properties.In addition, we will present possible directions for future research.

arXiv:1702.05799Nanosystems Physics Chemistry MathematicsFeb 20, 20170 citations

Optimal covariant measurement of momentum on a half line in quantum mechanics

Yutaka Shikano, Akio Hosoya

We cannot perform the projective measurement of a momentum on a half line since it is not an observable. Nevertheless, we would like to obtain some physical information of the momentum on a half line. We define an optimality for measurement as minimizing the variance between an inferred outcome of the measured system before a measuring process and a measurement outcome of the probe system after the measuring process, restricting our attention to the covariant measurement studied by Holevo [Rep. Math. Phys. 13, 379 (1978)]. Extending the domain of the momentum operator on a half line by introducing a two dimensional Hilbert space to be tensored, we make it self-adjoint and explicitly construct a model Hamiltonian for the measured and probe systems. By taking the partial trace over the newly introduced Hilbert space, the optimal covariant positive operator valued measure of a momentum on a half line is reproduced. We physically describe the measuring process to optimally evaluate the momentum of a particle on a half line.We cannot perform the projective measurement of a momentum on a half line since it is not an observable. Nevertheless, we would like to obtain some physical information of the momentum on a half line. We define an optimality for measurement as minimizing the variance between an inferred outcome of the measured system before a measuring process and a measurement outcome of the probe system after the measuring process, restricting our attention to the covariant measurement studied by Holevo [Rep. Math. Phys. 13, 379 (1978)]. Extending the domain of the momentum operator on a half line by introducing a two dimensional Hilbert space to be tensored, we make it self-adjoint and explicitly construct a model Hamiltonian for the measured and probe systems. By taking the partial trace over the newly introduced Hilbert space, the optimal covariant positive operator valued measure of a momentum on a half line is reproduced. We physically describe the measuring process to optimally evaluate the momentum of a particle on a half line.

arXiv:0710.1724Journal of Mathematical PhysicsMay 1, 20088 citations

Two-Particle Systems, Potential-Well Bound-State Problems

F. S. Levin

Cambridge University Press eBooksDec 3, 20010 citations

Some Exact Results for a Two-Dimensional System of Particles

Robert M. Sinclair

Few-Body SystemsJan 1, 19950 citations

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