On Scattering and Bound States for a Singular Potential

Ferreira, Erasmo; Sesma, J.; Torres, P. L.

doi:10.1143/ptp.43.1

Cited by 6 publications

(2 citation statements)

References 6 publications

(6 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…as the radial part of the Laplacian in any dimension. Their eigenfunctions can be expressed in terms of Bessel-type functions, and they have a surprisingly long and intricate theory, see for example [8,9,12,14,25,29]. It is natural to try to interpret (1.1) as a closed operator on L 2 (R + ).…”

Section: Introductionmentioning

confidence: 99%

On Schrödinger Operators with Inverse Square Potentials on the Half-Line

Dereziński

Richard

2016

Ann. Henri Poincaré

135

View full text Add to dashboard Cite

Abstract. The paper is devoted to operators given formally by the expressionThis expression is homogeneous of degree minus 2. However, when we try to realize it as a self-adjoint operator for real α, or closed operator for complex α, we find that this homogeneity can be broken. This leads to a definition of two holomorphic families of closed operators on L 2 (R+), which we denote Hm,κ and H ν 0 , with m 2 = α, −1 < Re(m) < 1, and where κ, ν ∈ C ∪{∞} specify the boundary condition at 0. We study these operators using their explicit solvability in terms of Bessel-type functions and the Gamma function. In particular, we show that their point spectrum has a curious shape: a string of eigenvalues on a piece of a spiral. Their continuous spectrum is always [0, ∞[. Restricted to their continuous spectrum, we diagonalize these operators using a generalization of the Hankel transformation. We also study their scattering theory. These operators are usually non-self-adjoint. Nevertheless, it is possible to use concepts typical for the self-adjoint case to study them. Let us also stress that −1 < Re(m) < 1 is the maximal region of parameters for which the operators Hm,κ can be defined within the framework of the Hilbert space L 2 (R+).

show abstract

Section: Introductionmentioning

confidence: 99%

On Schrödinger Operators with Inverse Square Potentials on the Half-Line

Dereziński

Richard

2016

Ann. Henri Poincaré

135

View full text Add to dashboard Cite

show abstract

“…One of the well-known such quantum mechanical models is the Calogero model [134,135] which is the multi-particle system with the pairwise inversesquare interaction 6 . It was firstly proven in [148,149] that the Calogero model has 5 The treatment of the inverse-square potential in quantum mechanics was discussed in [55,56,57,58,59,60,61,62,63,64]. 6 See [136,137,138] for the enlightening reviews on (super)conformal mechanics and also see [139,140,141,142,143,144,145,146,147] for excellent reviews on the Calogero model.…”

Section: Historical Backgroundmentioning

confidence: 99%

Superconformal Quantum Mechanics from M2-branes

Okazaki

2015

Preprint

View full text Add to dashboard Cite

We discuss the superconformal quantum mechanics arising from the M2-branes. We begin with a comprehensive review on the superconformal quantum mechanics and emphasize that conformal symmetry and supersymmetry in quantum mechanics contain a number of exotic and enlightening properties which do not occur in higher dimensional field theories. We see that superfield and superspace formalism is available for N ≤ 8 superconformal mechanical models. We then discuss the M2-branes with a focus on the world-volume descriptions of the multiple M2-branes which are superconformal three-dimensional Chern-Simons matter theories. Finally we argue that the two topics are connected in M-theoretical construction by considering the multiple M2-branes wrapped around a compact Riemann surface and study the emerging IR quantum mechanics. We establish that the resulting quantum mechanics realizes a set of novel N ≥ 8 superconformal quantum mechanical models which have not been reached so far. Also we discuss possible applications of the superconformal quantum mechanics to mathematical physics.

show abstract

Stability and protonation of multielectron systems: The concept of proton affinity. I. Vague limits

Kryachko

2010

Int J of Quantum Chemistry

View full text Add to dashboard Cite

The present work is a kind of a ''polyphonic'' collection of thoughts about the relationship between the stability of multi-electron systems and the protonation. The intricacy of the protonation sites and the protonated states that are absorbed into the concept of the proton affinity is discussed, particularly addressing its range of validity. This work can also be considered as an attempt to have a look ''at different angles'' at one of the most important molecular processes that occur in nature and that are reflected in our mirror of the perception of nature.

show abstract

On Scattering and Bound States for a Singular Potential

Cited by 6 publications

References 6 publications

On Schrödinger Operators with Inverse Square Potentials on the Half-Line

On Schrödinger Operators with Inverse Square Potentials on the Half-Line

Superconformal Quantum Mechanics from M2-branes

Stability and protonation of multielectron systems: The concept of proton affinity. I. Vague limits

Contact Info

Product

Resources

About