3,583 research outputs found
Vapor pressure and evaporation rate of certain heat-resistant compounds in a vacuum at high temperatures
The vapor pressure and evaporation rate of borides of titanium, zirconium, and chrome; and of strontium and carbides of titanium, zirconium, and chrome, molybdenum silicide; and nitrides of titanium, niobium, and tantalum in a vacuum were studied. It is concluded that all subject compounds evaporate by molecular structures except AlB sub 12' which dissociates, losing the aluminum
SUSY transformations with complex factorization constants. Application to spectral singularities
Supersymmetric (SUSY) transformation operators corresponding to complex
factorization constants are analyzed as operators acting in the Hilbert space
of functions square integrable on the positive semiaxis. Obtained results are
applied to Hamiltonians possessing spectral singularities which are
non-Hermitian SUSY partners of selfadjoint operators. A new regularization
procedure for the resolution of the identity operator in terms of continuous
biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed.
It is also shown that the continuous spectrum eigenfunction has zero binorm (in
the sense of distributions) at the singular point.Comment: Thanks to A. Sokolov a number of inaccuracies are correcte
Supersymmetry of the Nonstationary Schr\"odinger equation and Time-Dependent Exactly Solvable Quantum Models
New exactly solvable quantum models are obtained with the help of the
supersymmetric extencion of the nonstationary Schr/"odinger equation.Comment: Talk at the 8th International Conference "Symmetry Methods in
Physics". Dubna, Russia, 28 July - 2 August, 199
Darboux transformations of coherent states of the time-dependent singular oscillator
Darboux transformation of both Barut-Girardello and Perelomov coherent states
for the time-dependent singular oscillator is studied. In both cases the
measure that realizes the resolution of the identity operator in terms of
coherent states is found and corresponding holomorphic representation is
constructed. For the particular case of a free particle moving with a fixed
value of the angular momentum equal to two it is shown that Barut-Giriardello
coherent states are more localized at the initial time moment while the
Perelomov coherent states are more stable with respect to time evolution. It is
also illustrated that Darboux transformation may keep unchanged this different
time behavior.Comment: 13 page
Connection between the Green functions of the supersymmetric pair of Dirac Hamiltonians
The Sukumar theorem about the connection between the Green functions of the
supersymmetric pair of the Schr\"odinger Hamiltonians is generalized to the
case of the supersymmetric pair of the Dirac Hamiltonians.Comment: 12 pages,Latex, no figure
Supersymmetric transformations for coupled channels with threshold differences
The asymptotic behaviour of the superpotential of general SUSY
transformations for a coupled-channel Hamiltonian with different thresholds is
analyzed. It is shown that asymptotically the superpotential can tend to a
diagonal matrix with an arbitrary number of positive and negative entries
depending on the choice of the factorization solution. The transformation of
the Jost matrix is generalized to "non-conservative" SUSY transformations
introduced in Sparenberg et al (2006 J. Phys. A: Math. Gen. 39 L639). Applied
to the zero initial potential the method permits to construct superpartners
with a nontrivially coupled Jost-matrix. Illustrations are given for two- and
three-channel cases.Comment: 17 pages, 3 explicit examples and figures adde
Utilization of the wastes of vital activity
The recycling of wastes from the biological complex for use in life-support systems is discussed. Topics include laboratory equipment, heat treatment of waste materials, mineralization of waste products, methods for production of ammonium hydroxide and nitric acid, the extraction of sodium chloride from mineralized products, and the recovery of nutrient substances for plants from urine
Darboux transformations for quasi-exactly solvable Hamiltonians
We construct new quasi-exactly solvable one-dimensional potentials through
Darboux transformations. Three directions are investigated:
Reducible and two types of irreducible second-order transformations. The
irreducible transformations of the first type give singular intermediate
potentials and the ones of the second type give complex-valued intermediate
potentials while final potentials are meaningful in all cases.
These developments are illustrated on the so-called radial sextic oscillator.Comment: 11 pages, Late
Exact propagators for SUSY partners
Pairs of SUSY partner Hamiltonians are studied which are interrelated by
usual (linear) or polynomial supersymmetry. Assuming the model of one of the
Hamiltonians as exactly solvable with known propagator, expressions for
propagators of partner models are derived. The corresponding general results
are applied to "a particle in a box", the Harmonic oscillator and a free
particle (i.e. to transparent potentials).Comment: 31 page
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