Approximate Eigensolutions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo>(</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:mfrac><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mo>[</mm

Hulthén, Lamek; Laurikainen, Kalervo V.

doi:10.1103/revmodphys.23.1

Cited by 138 publications

(20 citation statements)

References 6 publications

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“…The relation between the coupling constant, g, and the energy E for the ground state has been thoroughly studied before using other approximate methods [5,6]. We do not intend to reach the same precision as these methods exhibit for this particular potential, but mainly we want to furnish an idea about how the method behaves in this case when the order of approximation 2 increases.…”

Section: ~0mentioning

confidence: 99%

Approximate solution of bound state problems through continued fractions

Garibotti

Mignaco

1975

Z Physik A

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Abstract. A method to solve ordinary linear differential equations through continued fractions is applied to several physical systems. In particular, results for the Schr6dinger equation give a good accuracy for the eigenvalues of bound states in the S-wave Yukawa potential, and the lowest order approximations provide exact-values for the harmonic oscillator and Coulomb potential eigenvalues and eigenfunctions.

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Section: ~0mentioning

confidence: 99%

Approximate solution of bound state problems through continued fractions

Garibotti

Mignaco

1975

Z Physik A

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“…is the Fourier transform of the Hulthén wave function [33] (e −ar −e −br )/r with the parameters [34] …”

Section: Other Deuteron Wave Functionsmentioning

confidence: 99%

Meaning of the nuclear wave function

Terry

Miller

2016

Phys. Rev. C

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Background The intense current experimental interest in studying the structure of the deuteron and using it to enable accurate studies of neutron structure motivate us to examine the fourdimensional space-time nature of the nuclear wave function, and the various approximations used to reduce it to an object that depends only on three spatial variables.Purpose The aim is to determine if the ability to understand and analyze measured experimental cross sections is compromised by making the reduction from four to three dimensions.Method Simple, exactly-calculable, covariant models of a bound-state wave state wave function (a scalar boson made of two constituent-scalar bosons) with parameters chosen to represent a deuteron are used to investigate the accuracy of using different approximations to the nuclear wave function to compute the quasi-elastic scattering cross section. Four different versions of the wave function are defined (light-front spectator, light-front, light-front with scaling and non-relativistic) and used to compute the cross sections as a function of how far off the mass-shell (how virtual) is the struck constituent.Results We show that making an exact calculation of the quasi-elastic scattering cross section, involves using the light-front spectator wave function. All of the other approaches fail to reproduce the model exact calculation if the value of Bjorken x differs from unity. The model is extended to consider an essential effect of spin to show that constituent nucleons cannot be treated as being on their mass shell even when taking the matrix element of a 'good' current.Conclusions Developing realistic light-front spectator wave functions to meet the needs of current and planned experiments is a worthwhile activity.

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“…For this potential, the condition that a bound state exist is (Hulthen and Laurikainen, 1951) Mott argues that localized states will not exist if is smaller than the value on the right side of (5.4.45). For this potential, the condition that a bound state exist is (Hulthen and Laurikainen, 1951) Mott argues that localized states will not exist if is smaller than the value on the right side of (5.4.45).…”

Section: V(r) = (-E^/kr)e-^'mentioning

confidence: 99%

Impurities and Alloys

Callaway

1991

Quantum Theory of the Solid State

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Approximate Eigensolutions of(d2φdx2)+[

Cited by 138 publications

References 6 publications

Approximate solution of bound state problems through continued fractions

Approximate solution of bound state problems through continued fractions

Meaning of the nuclear wave function

Impurities and Alloys

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