1,560 research outputs found

### On Integrability and Pseudo-Hermitian Systems with Spin-Coupling Point Interactions

We study the pseudo-Hermitian systems with general spin-coupling point
interactions and give a systematic description of the corresponding boundary
conditions for PT-symmetric systems. The corresponding integrability for both
bosonic and fermionic many-body systems with PT-symmetric contact interactions
is investigated.Comment: 7 page

### p-Adic Schr\"{o}dinger-Type Operator with Point Interactions

A $p$-adic Schr\"{o}dinger-type operator $D^{\alpha}+V_Y$ is studied.
$D^{\alpha}$ ($\alpha>0$) is the operator of fractional differentiation and
$V_Y=\sum_{i,j=1}^nb_{ij}\delta_{x_i}$
$(b_{ij}\in\mathbb{C})$ is a singular potential containing the Dirac delta
functions $\delta_{x}$ concentrated on points $\{x_1,...,x_n\}$ of the field of
$p$-adic numbers $\mathbb{Q}_p$. It is shown that such a problem is well-posed
for $\alpha>1/2$ and the singular perturbation $V_Y$ is form-bounded for
$\alpha>1$. In the latter case, the spectral analysis of $\eta$-self-adjoint
operator realizations of $D^{\alpha}+V_Y$ in $L_2(\mathbb{Q}_p)$ is carried
out

### Remarks on some new models of interacting quantum fields with indefinite metric

We study quantum field models in indefinite metric. We introduce the modified
Wightman axioms of Morchio and Strocchi as a general framework of indefinite
metric quantum field theory (QFT) and present concrete interacting relativistic
models obtained by analytical continuation from some stochastic processes with
Euclidean invariance. As a first step towards scattering theory in indefinite
metric QFT, we give a proof of the spectral condition on the translation group
for the relativistic models.Comment: 13 page

### Many Body Problems with "Spin"-Related Contact Interactions

We study quantum mechanical systems with "spin"-related contact interactions
in one dimension. The boundary conditions describing the contact interactions
are dependent on the spin states of the particles. In particular we investigate
the integrability of $N$-body systems with $\delta$-interactions and point spin
couplings. Bethe ansatz solutions, bound states and scattering matrices are
explicitly given. The cases of generalized separated boundary condition and
some Hamiltonian operators corresponding to special spin related boundary
conditions are also discussed.Comment: 13 pages, Late

### Four-Parameter Point-Interaction in 1-D Quantum Systems

We construct a four-parameter point-interaction for a non-relativistic
particle moving on a line as the limit of a short range interaction with range
tending toward zero. For particular choices of the parameters, we can obtain a
delta-interaction or the so-called delta'-interaction. The Hamiltonian
corresponding to the four-parameter point-interaction is shown to correspond to
the four-parameter self-adjoint Hamiltonian of the free particle moving on the
line with the origin excluded.Comment: 6 pages, Plain Tex file. BU-HEP-92-

### Distribution theory for Schr\"odinger's integral equation

Much of the literature on point interactions in quantum mechanics has focused
on the differential form of Schr\"odinger's equation. This paper, in contrast,
investigates the integral form of Schr\"odinger's equation. While both forms
are known to be equivalent for smooth potentials, this is not true for
distributional potentials. Here, we assume that the potential is given by a
distribution defined on the space of discontinuous test functions.
First, by using Schr\"odinger's integral equation, we confirm a seminal
result by Kurasov, which was originally obtained in the context of
Schr\"odinger's differential equation. This hints at a possible deeper
connection between both forms of the equation. We also sketch a generalisation
of Kurasov's result to hypersurfaces.
Second, we derive a new closed-form solution to Schr\"odinger's integral
equation with a delta prime potential. This potential has attracted
considerable attention, including some controversy. Interestingly, the derived
propagator satisfies boundary conditions that were previously derived using
Schr\"odinger's differential equation.
Third, we derive boundary conditions for `super-singular' potentials given by
higher-order derivatives of the delta potential. These boundary conditions
cannot be incorporated into the normal framework of self-adjoint extensions. We
show that the boundary conditions depend on the energy of the solution, and
that probability is conserved.
This paper thereby confirms several seminal results and derives some new
ones. In sum, it shows that Schr\"odinger's integral equation is viable tool
for studying singular interactions in quantum mechanics.Comment: 23 page

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