scholarly journals Properties of Stark Resonant States in Exactly Solvable Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jeffrey M. Brown ◽  
Miroslav Kolesik
Keyword(s):  
Integration Method ◽  
Biorthogonal System ◽  
Outgoing Wave ◽  
Airy Functions ◽  
One Dimensional ◽  
Resonant States ◽  
Exactly Solvable ◽  
Spatial Dimensions ◽  
Analytic Expressions ◽  
Wave Boundary

Properties of Stark resonant states are studied in two exactly solvable systems. These resonances are shown to form a biorthogonal system with respect to a pairing defined by a contour integral that selects states with outgoing wave boundary conditions. Analytic expressions are derived for the pseudonorm, dipole moment, and coupling matrix elements which relate systems with different strengths of the external field. All results are based on explicit calculations made possible by a newly designed integration method for combinations of Airy functions representing resonant eigenstates. Generalizations for one-dimensional systems with short-range potentials are presented, and relations are identified which are likely to hold in systems with three spatial dimensions.

scholarly journals RESONANT STATES IN A ONE-DIMENSIONAL QUANTUM SYSTEM

2020 ◽  
Vol 4 (3) ◽  
pp. 300-304
Author(s):  
A. Tanimu ◽  
I. M. Bagudo
Keyword(s):  
Bound States ◽  
Outgoing Wave ◽  
Complex Solution ◽  
One Dimensional ◽  
Resonant States ◽  
Newton Raphson ◽  
Transcendental Equations ◽  
The One ◽  
Wave Boundary ◽  
Raphson Method

In this work, the concept of resonant states (RSs) in a finite square quantum well is presented. We first derive the analytic secular transcendental equations for even and odd states by applying the outgoing wave boundary conditions into the one-dimensional Schrödinger’s wave equation. The complex solution of these equations is found using the numerical Newton-Raphson method implemented in MATLAB. We can see in particular, that the RSs present a general class of Eigenstates, which includes bound states, anti-bound states, and normal RSs.

scholarly journals QUASI-EXACT SOLVABILITY OF PLANAR DIRAC ELECTRON IN COULOMB AND MAGNETIC FIELDS

2005 ◽  
Vol 20 (09) ◽  
pp. 673-679 ◽  
Author(s):  
CHUN-MING CHIANG ◽  
CHOON-LIN HO
Keyword(s):  
Differential Equation ◽  
Dirac Equation ◽  
Magnetic Fields ◽  
One Dimensional ◽  
Exact Solvability ◽  
Exactly Solvable ◽  
Spatial Dimensions ◽  
Dirac Electron

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is a physical example of quasi-exactly solvable systems. This model, however, does not belong to the classes based on the algebra sl (2) which underlies most one-dimensional and effectively one-dimensional quasi-exactly solvable systems. In this paper we demonstrate that the quasi-exactly solvable differential equation possesses a hidden osp (2,2) superalgebra.

SUPERSYMMETRIC APPROACH TO QUASINORMAL MODES

2008 ◽  
Vol 23 (10) ◽  
pp. 751-760
Author(s):  
T. K. JANA ◽  
P. ROY
Keyword(s):  
Gordon Equation ◽  
Quasinormal Modes ◽  
Outgoing Wave ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Klein Gordon ◽  
Wave Boundary ◽  
Klein Gordon Equation ◽  
Supersymmetric Approach

Supersymmetry (SUSY) in quantum mechanics is extended from square integrable states to those satisfying the outgoing wave boundary condition. Using this formalism we obtain new exactly solvable potentials admitting quasinormal modes (QNM) solutions of the Klein–Gordon equation.

Kompressionswellen in einer isothermen Atmosphäre mit vertikalem Magnetfeld

1966 ◽  
Vol 21 (7) ◽  
pp. 1098-1106 ◽  
Author(s):  
R. Lust ◽  
M. Scholer
Keyword(s):  
Magnetic Field ◽  
Strong Influence ◽  
Vertical Direction ◽  
Time Dependent ◽  
Solar Chromosphere ◽  
Magnetohydrodynamic Equation ◽  
One Dimensional ◽  
Spatial Dimensions ◽  
Propagation Of Waves ◽  
The Waves

The propagation of waves in the solar atmosphere is investigated with respect to the problem of the chromospheric spiculae and of the heating of the solar chromosphere and corona. In particular the influence of external magnetic fields is considered. Waves of finite amplitudes are numerically calculated by solving the time-dependent magnetohydrodynamic equation for two spatial dimensions by assuming axial symmetry. For the case without a magnetic field the comparison between one dimensional and two dimensional treatment shows the strong influence of the radial propagation on the steepening of waves in the vertical direction. In the presence of a magnetic field it is shown that the propagation is strongly guided along the lines of force. The steepening of the waves along the field is much larger as compared to the case where no field is present.

scholarly journals EXACTLY SOLVABLE MODELS THROUGH THE GENERALIZED EMPTY INTERVAL METHOD: MULTI-SPECIES AND MORE-THAN-TWO-SITE INTERACTIONS

2004 ◽  
Vol 18 (14) ◽  
pp. 2047-2055 ◽  
Author(s):  
AMIR AGHAMOHAMMADI ◽  
MOHAMMAD KHORRAMI
Keyword(s):  
Reaction Diffusion ◽  
Solvable Models ◽  
Empty Interval ◽  
Interval Method ◽  
One Dimensional ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Exactly Solvable ◽  
Necessary And Sufficient ◽  
Time Evolution Equation

Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closure of the time evolution equation for [Formula: see text], the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time t.

Mass Flow and Thrust Performance of Nozzles With Mixed and Unmixed Nonuniform Flow

1995 ◽  
Vol 117 (4) ◽  
pp. 617-622 ◽  
Author(s):  
Reiner Decher
Keyword(s):  
Mass Flow ◽  
Total Pressure ◽  
Nonuniform Flow ◽  
Flow Properties ◽  
One Dimensional ◽  
Flow Equations ◽  
Design Variables ◽  
Analytic Expressions ◽  
The One ◽  
Thrust Performance

The calculated thrust and mass flow rate of a nozzle depend on the uniformity of the entering flow. The one-dimensional flow equations are extended to arrive at analytic expressions for the predicted performance of a nozzle processing two streams whose properties are determined ahead of the throat. The analysis approach forms the basis for the understanding of flows which have more complex distributions of total pressure and temperature. The uncertainty associated with mixing is examined by the consideration of the two limiting cases: compound flow with no mixing and completely mixed flow. Nozzle discharge and velocity coefficients accounting for non-uniformity are derived. The methodology can be extended to experimentally measured variations of flow properties so that proper geometric design variables may be obtained.

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