Comment on: “Bound-State Energies of a Particle in a Finite Square Well”

1971 ◽  
Vol 39 (8) ◽  
pp. 976-976
Author(s):  
James J. Murphy
Keyword(s):  
Bound State ◽  
Square Well

scholarly journals Quantum star-graph analogues of PT-symmetric square wells

2012 ◽  
Vol 90 (12) ◽  
pp. 1287-1293 ◽  
Author(s):  
Miloslav Znojil
Keyword(s):  
Boundary Conditions ◽  
Bound State ◽  
Robin Boundary Conditions ◽  
Star Graph ◽  
The Real ◽  
Rotation Symmetric ◽  
Symmetric Quantum ◽  
Symmetric Square ◽  
Square Well ◽  
Robin Boundary

We recall the solvable [Formula: see text]-symmetric quantum square well on an interval of x ∈ (–L, L) := [Formula: see text] (with an α-dependent non-Hermiticity given by Robin boundary conditions) and generalize it. In essence, we just replace the support interval [Formula: see text] (reinterpreted as an equilateral two-pointed star graph with Kirchhoff matching at the vertex x = 0) with a q-pointed equilateral star graph [Formula: see text] endowed with the simplest complex-rotation-symmetric external α-dependent Robin boundary conditions. The remarkably compact form of the secular determinant is then deduced. Its analysis reveals that (i) at any integer q = 2, 3, …, there exists the same q-independent and infinite subfamily of the real energies, and (ii) at any special q = 2, 6, 10, …, there exists another, additional, q-dependent infinite subfamily of the real energies. In the spirit of the recently proposed dynamical construction of the Hilbert space of a quantum system, the physical bound-state interpretation of these eigenvalues is finally proposed.

Square-well potential and three-nucleon bound-state properties

1971 ◽  
Vol 34 (3) ◽  
pp. 184-186 ◽  
Author(s):  
R. Van Wageningen ◽  
G. Erens
Keyword(s):  
Bound State ◽  
Square Well

Bound‐state eigenvalues of the square‐well potential

1976 ◽  
Vol 44 (6) ◽  
pp. 574-576 ◽  
Author(s):  
R. D. Murphy ◽  
J. M. Phillips
Keyword(s):  
Bound State ◽  
Square Well

scholarly journals ON THE COMMON LIMIT OF THE PT-SYMMETRIC ROSEN–MORSE II AND FINITE SQUARE WELL POTENTIALS

2017 ◽  
Vol 57 (6) ◽  
pp. 412
Author(s):  
József Kovács ◽  
Géza Lévai
Keyword(s):  
Energy Spectrum ◽  
State Energy ◽  
Mathematical Structure ◽  
Bound State ◽  
Transmission And Reflection Coefficients ◽  
Common Limit ◽  
Symmetric Square ◽  
The Common ◽  
Square Well ◽  
Transmission And Reflection

Two <em>PT</em>-symmetric potentials are compared, which possess asymptotically finite imaginary components: the <em>PT</em>-symmetric Rosen-Morse II and the finite <em>PT</em>-symmetric square well potentials. Despite their different mathematical structure, their shape is rather similar, and this fact leads to similarities in their physical characteristics. Their bound-state energy spectrum was found to be purely real, an this finding was attributed to their <br />asymptotically non-vanishing imaginary potential components. Here the <em>V(x</em>)= <em>γδ</em>(<em>x</em>)+ i2Λ sgn(<em>x</em>) potential is discussed, which can be obtained as the common limit of the two other potentials. The energy spectrum, the bound-state wave functions and the transmission and reflection coefficients are studied in the respective limits, and the results are compared.

NONLOCAL SEPARABLE SOLUTIONS OF THE INVERSE SCATTERING PROBLEM

1993 ◽  
Vol 08 (18) ◽  
pp. 3163-3184 ◽  
Author(s):  
TONY GHERGHETTA ◽  
YOICHIRO NAMBU
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Bound State ◽  
Separable Potential ◽  
Nonlocal Potential ◽  
S Wave ◽  
Weakly Bound ◽  
Square Well ◽  
Nonlocal Separable Potential

We extend the nonlocal separable potential solutions of Gourdin and Martin for the inverse scattering problem to the case where sin δ0 has more than N zeroes, δ0 being the s-wave scattering phase shift and δ0(0) − δ0(∞) = Nπ. As an example we construct the solution for the particular case of 4 He and show how to incorporate a weakly bound state. Using a local square well potential chosen to mimic the real 4 He potential, we compare the off-shell extension of the nonlocal potential solution with the exactly solvable square well. We then discuss how a nonlocal potential might be used to simplify the many-body problem of liquid 4 He .

Electromigration Force on a Proton with a Bound State

2010 ◽  
Vol 295-296 ◽  
pp. 69-77
Author(s):  
A. Lodder
Keyword(s):  
Driving Force ◽  
Electron Gas ◽  
Bound State ◽  
Wind Force ◽  
Sign Change ◽  
Well Model ◽  
Self Consistent ◽  
Supplementary Term ◽  
Different Depths ◽  
Square Well

The driving force on an ion in a metal due to an applied electric field, called the electromigration force, is built up out of two contributions, a wind force and a direct force. The wind force is due to the scattering of the current carrying electrons off the ion. The direct force works on the effective charge of the ion. In the present work we concentrate on the direct force on a migrating proton embedded in an electron gas. For this force a sign change is obtained as soon as a bound state is formed. In recent calculations hardly a sign change was seen, although a bound state was found in a self-consistent-potential for lower electron densities. Here we show that a supplementary term shows up, as soon as one accounts for the bound state explicitly. By this the problem has been solved regarding a possible lack of completeness of the published formalism. The results presented are based on square-well model potentials. By using different depths it is possible to show results for potentials without a bound state and accommodating one bound state.

Two-body Dirac equation: illustration in one space dimension

1988 ◽  
Vol 66 (9) ◽  
pp. 769-775 ◽  
Author(s):  
F. A. B. Coutinho ◽  
W. Glöckle ◽  
Y. Nogami ◽  
F. M. Toyama
Keyword(s):  
Dirac Equation ◽  
Space Dimension ◽  
Bound State ◽  
Sharp Edge ◽  
Finite Range ◽  
Range Interaction ◽  
Square Well ◽  
The One ◽  
The Masses ◽  
One Space Dimension

Various features that are characteristic of the two-body Dirac equation but not of the one-body Dirac equation are illustrated by means of solvable examples (mainly square-well potentials) in one space dimension. For the Lorentz character of the potential there are three types; vector, scalar, and pseudoscalar. We classify the bound-state solutions as normal and abnormal. As the interaction is adiabatically switched off, the energy of the normal solutions reaches 2m (the sum of the masses of the constituent particles), whereas the energy of the abnormal solutions becomes zero. When the sharp edge of the square-well potential is smeared out, some of the solutions become unnormalizable and hence unacceptable. This leads to a certain restriction on the choice of the potential. The two-body Dirac equation with a finite-range interaction is not exactly covariant. The degree of noncovariance is examined.

scholarly journals A simplified response function formalism for medium-heavy Λ hypernuclei

2019 ◽  
Vol 11 ◽  
Author(s):  
Theodora Petridou
Keyword(s):  
Response Function ◽  
Optical Potential ◽  
Plane Waves ◽  
Bound State ◽  
Green Function Method ◽  
Neutron Hole ◽  
Proposed Model ◽  
Square Well ◽  
The Green Function ◽  
Experimental Values

There is a variety of spectra for Λ hypernuclei (from light to heavy) which contain many peaks ranging from the deepest orbits to the surface ones. An approach is presented for the calculation of the bound state specrum of Λ hypernuclei, where the cross section is expressed through the response function. This was achieved in the framework of the Green function method with a square well optical potential using the plane waves. An analytic treatment was made for the prominent peaks with the contribution of only the valence neutron-hole series and a Gaussian folding was obtained for the rest spectrum. The method was applied mainly to the (π+,Κ+) medium to heavy Λ hypernuclei and also to the (Ä"~in-flight, π~) Λ hypernuclear spectra (with respect to their differences). The results are satisfactory compared to the experimental values. The main advantage of the proposed model is its simplicity. Possible extensions and improvements of this method are also suggested.

Scalar Potentials and the Dirac Equation

1994 ◽  
Vol 49 (11) ◽  
pp. 997-1012 ◽  
Author(s):  
Bastian Bergerhoff ◽  
Gerhard Soff
Keyword(s):  
Dirac Equation ◽  
Bound State ◽  
Wave Functions ◽  
Relativistic Wave ◽  
Quark Confinement ◽  
Energy Eigenvalues ◽  
Quadratic Potentials ◽  
Square Well ◽  
Scalar Potentials ◽  
Continuum Wave

Abstract The Dirac equation is solved for various types of scalar potentials. Energy eigenvalues and normalized bound-state wave functions are calculated analytically for a scalar 1 / r-potential as well as for a mixed scalar and Coulomb 1 / r-potential. Also continuum wave functions for positive and negative energies are derived. Similarly, we investigate the solutions of the Dirac equation for a scalar square-well potential. Relativistic wave functions for scalar Yukawa and exponential potentials are determined numerically. Finally, we also discuss solutions of the Dirac equation for scalar linear and quadratic potentials which are frequently used to simulate quark confinement.

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