7,191 research outputs found
Sufficient conditions for the existence of bound states in a central potential
We show how a large class of sufficient conditions for the existence of bound
states, in non-positive central potentials, can be constructed. These
sufficient conditions yield upper limits on the critical value,
, of the coupling constant (strength), , of the
potential, , for which a first -wave bound state appears.
These upper limits are significantly more stringent than hitherto known
results.Comment: 7 page
ILC Operating Scenarios
The ILC Technical Design Report documents the design for the construction of
a linear collider which can be operated at energies up to 500 GeV. This report
summarizes the outcome of a study of possible running scenarios, including a
realistic estimate of the real time accumulation of integrated luminosity based
on ramp-up and upgrade processes. The evolution of the physics outcomes is
emphasized, including running initially at 500 GeV, then at 350 GeV and 250
GeV. The running scenarios have been chosen to optimize the Higgs precision
measurements and top physics while searching for evidence for signals beyond
the standard model, including dark matter. In addition to the certain precision
physics on the Higgs and top that is the main focus of this study, there are
scientific motivations that indicate the possibility for discoveries of new
particles in the upcoming operations of the LHC or the early operation of the
ILC. Follow-up studies of such discoveries could alter the plan for the
centre-of-mass collision energy of the ILC and expand the scientific impact of
the ILC physics program. It is envisioned that a decision on a possible energy
upgrade would be taken near the end of the twenty year period considered in
this report
Necessary and sufficient conditions for existence of bound states in a central potential
We obtain, using the Birman-Schwinger method, a series of necessary
conditions for the existence of at least one bound state applicable to
arbitrary central potentials in the context of nonrelativistic quantum
mechanics. These conditions yield a monotonic series of lower limits on the
"critical" value of the strength of the potential (for which a first bound
state appears) which converges to the exact critical strength. We also obtain a
sufficient condition for the existence of bound states in a central monotonic
potential which yield an upper limit on the critical strength of the potential.Comment: 7 page
Critical strength of attractive central potentials
We obtain several sequences of necessary and sufficient conditions for the
existence of bound states applicable to attractive (purely negative) central
potentials. These conditions yields several sequences of upper and lower limits
on the critical value, , of the coupling constant
(strength), , of the potential, , for which a first
-wave bound state appears, which converges to the exact critical value.Comment: 18 page
A revision of the Generalized Uncertainty Principle
The Generalized Uncertainty Principle arises from the Heisenberg Uncertainty
Principle when gravity is taken into account, so the leading order correction
to the standard formula is expected to be proportional to the gravitational
constant . On the other hand, the emerging picture suggests a
set of departures from the standard theory which demand a revision of all the
arguments used to deduce heuristically the new rule. In particular, one can now
argue that the leading order correction to the Heisenberg Uncertainty Principle
is proportional to the first power of the Planck length . If so, the
departures from ordinary quantum mechanics would be much less suppressed than
what is commonly thought.Comment: 6 pages, 1 figur
Minimal Length and the Quantum Bouncer: A Nonperturbative Study
We present the energy eigenvalues of a quantum bouncer in the framework of
the Generalized (Gravitational) Uncertainty Principle (GUP) via quantum
mechanical and semiclassical schemes. In this paper, we use two equivalent
nonperturbative representations of a deformed commutation relation in the form
[X,P]=i\hbar(1+\beta P^2) where \beta is the GUP parameter. The new
representation is formally self-adjoint and preserves the ordinary nature of
the position operator. We show that both representations result in the same
modified semiclassical energy spectrum and agrees well with the quantum
mechanical description.Comment: 14 pages, 2 figures, to appear in Int. J. Theor. Phy
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