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Teaching schools evaluation. Research Brief
This Research Brief reports the findings from a two-year study (2013-15) in to the work of teaching schools and their alliances commissioned by the National College for Teaching and Leadership (NCTL). The broad aim of the study was to investigate the effectiveness and impact of teaching schools on improvement, and identify the quality and scope of external support that are required to enhance these . This was achieved through combining qualitative and quantitative data collection and analysis derived from three research activities: case studies of 26 teaching schools alliances (TSAs), a national survey of the first three cohorts of 345 TSAs, and secondary research and analysis of national performance and inspection results
Quantum oscillator on complex projective space (Lobachewski space) in constant magnetic field and the issue of generic boundary conditions
We perform a 1-parameter family of self-adjoint extensions characterized by
the parameter . This allows us to get generic boundary conditions for
the quantum oscillator on dimensional complex projective
space() and on its non-compact version i.e., Lobachewski
space() in presence of constant magnetic field. As a result, we
get a family of energy spectrums for the oscillator. In our formulation the
already known result of this oscillator is also belong to the family. We have
also obtained energy spectrum which preserve all the symmetry (full hidden
symmetry and rotational symmetry) of the oscillator. The method of self-adjoint
extensions have been discussed for conic oscillator in presence of constant
magnetic field also.Comment: Accepted in Journal of Physics
Self-Adjointness of Generalized MIC-Kepler System
We have studied the self-adjointness of generalized MIC-Kepler Hamiltonian,
obtained from the formally self-adjoint generalized MIC-Kepler Hamiltonian. We
have shown that for \tilde l=0, the system admits a 1-parameter family of
self-adjoint extensions and for \tilde l \neq 0 but \tilde l <{1/2}, it has
also a 1-parameter family of self-adjoint extensions.Comment: 11 pages, Latex, no figur
Schroedinger operators with singular interactions: a model of tunneling resonances
We discuss a generalized Schr\"odinger operator in , with an attractive singular interaction supported by a
-dimensional hyperplane and a finite family of points. It can be
regarded as a model of a leaky quantum wire and a family of quantum dots if
, or surface waves in presence of a finite number of impurities if .
We analyze the discrete spectrum, and furthermore, we show that the resonance
problem in this setting can be explicitly solved; by Birman-Schwinger method it
is cast into a form similar to the Friedrichs model.Comment: LaTeX2e, 34 page
Higher order Schrodinger and Hartree-Fock equations
The domain of validity of the higher-order Schrodinger equations is analyzed
for harmonic-oscillator and Coulomb potentials as typical examples. Then the
Cauchy theory for higher-order Hartree-Fock equations with bounded and Coulomb
potentials is developed. Finally, the existence of associated ground states for
the odd-order equations is proved. This renders these quantum equations
relevant for physics.Comment: 19 pages, to appear in J. Math. Phy
Some remarks on quasi-Hermitian operators
A quasi-Hermitian operator is an operator that is similar to its adjoint in
some sense, via a metric operator, i.e., a strictly positive self-adjoint
operator. Whereas those metric operators are in general assumed to be bounded,
we analyze the structure generated by unbounded metric operators in a Hilbert
space. Following our previous work, we introduce several generalizations of the
notion of similarity between operators. Then we explore systematically the
various types of quasi-Hermitian operators, bounded or not. Finally we discuss
their application in the so-called pseudo-Hermitian quantum mechanics.Comment: 18page
On elements of the Lax-Phillips scattering scheme for PT-symmetric operators
Generalized PT-symmetric operators acting an a Hilbert space
are defined and investigated. The case of PT-symmetric extensions of a
symmetric operator is investigated in detail. The possible application of
the Lax-Phillips scattering methods to the investigation of PT-symmetric
operators is illustrated by considering the case of 0-perturbed operators
Boundary conditions: The path integral approach
The path integral approach to quantum mechanics requires a substantial
generalisation to describe the dynamics of systems confined to bounded domains.
Non-local boundary conditions can be introduced in Feynman's approach by means
of boundary amplitude distributions and complex phases to describe the quantum
dynamics in terms of the classical trajectories. The different prescriptions
involve only trajectories reaching the boundary and correspond to different
choices of boundary conditions of selfadjoint extensions of the Hamiltonian.
One dimensional particle dynamics is analysed in detail.Comment: 8 page
Wigner quantization of some one-dimensional Hamiltonians
Recently, several papers have been dedicated to the Wigner quantization of
different Hamiltonians. In these examples, many interesting mathematical and
physical properties have been shown. Among those we have the ubiquitous
relation with Lie superalgebras and their representations. In this paper, we
study two one-dimensional Hamiltonians for which the Wigner quantization is
related with the orthosymplectic Lie superalgebra osp(1|2). One of them, the
Hamiltonian H = xp, is popular due to its connection with the Riemann zeros,
discovered by Berry and Keating on the one hand and Connes on the other. The
Hamiltonian of the free particle, H_f = p^2/2, is the second Hamiltonian we
will examine. Wigner quantization introduces an extra representation parameter
for both of these Hamiltonians. Canonical quantization is recovered by
restricting to a specific representation of the Lie superalgebra osp(1|2)
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