Pub Date : 1972-12-01DOI: 10.1088/0305-4470/5/12/002
J. Gibbon, J. C. Eilbeck
The asymptotic form of Hirota's N soliton solution of the Korteweg-de Vries equation is derived. The phase shifts of the N solitons caused by a general collision are found to be linear sums of two soliton terms.
{"title":"The asymptotic form of the N soliton solution of the Korteweg-de Vries equation","authors":"J. Gibbon, J. C. Eilbeck","doi":"10.1088/0305-4470/5/12/002","DOIUrl":"https://doi.org/10.1088/0305-4470/5/12/002","url":null,"abstract":"The asymptotic form of Hirota's N soliton solution of the Korteweg-de Vries equation is derived. The phase shifts of the N solitons caused by a general collision are found to be linear sums of two soliton terms.","PeriodicalId":54612,"journal":{"name":"Physics-A Journal of General and Applied Physics","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1972-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74443223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1972-12-01DOI: 10.1088/0305-4470/5/12/007
D. Crothers
Using the method of steepest descent an exact and practicable asymptotic expansion for the parabolic cylinder function Dp(z) is derived in the case when mod z mod 2 and mod p mod are both large and of the same order. Limitations and defects in the existing literature on the subject are reviewed. Two-term approximations of considerable importance in the phase-integral analysis of four-transition-point problems are obtained. Several examples required in the analysis of double underdense-potential-barrier problems are given. It is pointed out that such potential barrier problems are associated with perturbed symmetric resonance strong rotational coupling and curve-crossing in atom-atom collision theory. New model transition probabilities are presented.
{"title":"Asymptotic expansions for parabolic cylinder functions of large order and argument","authors":"D. Crothers","doi":"10.1088/0305-4470/5/12/007","DOIUrl":"https://doi.org/10.1088/0305-4470/5/12/007","url":null,"abstract":"Using the method of steepest descent an exact and practicable asymptotic expansion for the parabolic cylinder function Dp(z) is derived in the case when mod z mod 2 and mod p mod are both large and of the same order. Limitations and defects in the existing literature on the subject are reviewed. Two-term approximations of considerable importance in the phase-integral analysis of four-transition-point problems are obtained. Several examples required in the analysis of double underdense-potential-barrier problems are given. It is pointed out that such potential barrier problems are associated with perturbed symmetric resonance strong rotational coupling and curve-crossing in atom-atom collision theory. New model transition probabilities are presented.","PeriodicalId":54612,"journal":{"name":"Physics-A Journal of General and Applied Physics","volume":"35 1","pages":"1680-1688"},"PeriodicalIF":0.0,"publicationDate":"1972-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88933130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1972-11-01DOI: 10.1088/0305-4470/5/11/017
R. Burman
The energy densities and generalized Poynting vectors for longitudinal and transverse waves in cold plasmas are investigated.
研究了冷等离子体中纵波和横波的能量密度和广义坡印亭矢量。
{"title":"A photon rest mass and energy transport in cold plasmas","authors":"R. Burman","doi":"10.1088/0305-4470/5/11/017","DOIUrl":"https://doi.org/10.1088/0305-4470/5/11/017","url":null,"abstract":"The energy densities and generalized Poynting vectors for longitudinal and transverse waves in cold plasmas are investigated.","PeriodicalId":54612,"journal":{"name":"Physics-A Journal of General and Applied Physics","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1972-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79705946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1972-11-01DOI: 10.1088/0305-4470/5/11/011
A. Sirohi, M. K. Srivastava
A recent method, based on obtaining a first order nonlinear differential equation, to calculate the energy eigenvalues for a local potential has been improved. Two transformations which are capable of greater manoeuvrability and which reduce computational labour are suggested.
{"title":"Numerical calculation of the energy eigenvalues for a local potential","authors":"A. Sirohi, M. K. Srivastava","doi":"10.1088/0305-4470/5/11/011","DOIUrl":"https://doi.org/10.1088/0305-4470/5/11/011","url":null,"abstract":"A recent method, based on obtaining a first order nonlinear differential equation, to calculate the energy eigenvalues for a local potential has been improved. Two transformations which are capable of greater manoeuvrability and which reduce computational labour are suggested.","PeriodicalId":54612,"journal":{"name":"Physics-A Journal of General and Applied Physics","volume":"97 1","pages":"1639-1641"},"PeriodicalIF":0.0,"publicationDate":"1972-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85944852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1972-11-01DOI: 10.1088/0305-4470/5/11/015
J. Gibbon, J. C. Eilbeck
The authors suggest a possible N soliton solution for an equation of nonlinear optics (and hence, by a transformation, for the sine-Gordon equation). The proposed solution, which has been tested for N
{"title":"A possible N soliton solution for a nonlinear optics equation","authors":"J. Gibbon, J. C. Eilbeck","doi":"10.1088/0305-4470/5/11/015","DOIUrl":"https://doi.org/10.1088/0305-4470/5/11/015","url":null,"abstract":"The authors suggest a possible N soliton solution for an equation of nonlinear optics (and hence, by a transformation, for the sine-Gordon equation). The proposed solution, which has been tested for N<or=3, is a combination of simple functions similar to the N soliton solution of the Korteweg-de Vries equation.","PeriodicalId":54612,"journal":{"name":"Physics-A Journal of General and Applied Physics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1972-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85690854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1972-11-01DOI: 10.1088/0305-4470/5/11/003
W. Brown
The eigenvalues of perturbed Schrodinger equation with an odd perturbation are even functions of the perturbation parameter lambda . It is shown how to transform the perturbed equation so that the new perturbation is also explicitly an even function of lambda .
{"title":"Perturbation theory for odd perturbations","authors":"W. Brown","doi":"10.1088/0305-4470/5/11/003","DOIUrl":"https://doi.org/10.1088/0305-4470/5/11/003","url":null,"abstract":"The eigenvalues of perturbed Schrodinger equation with an odd perturbation are even functions of the perturbation parameter lambda . It is shown how to transform the perturbed equation so that the new perturbation is also explicitly an even function of lambda .","PeriodicalId":54612,"journal":{"name":"Physics-A Journal of General and Applied Physics","volume":"32 1","pages":"1563-1565"},"PeriodicalIF":0.0,"publicationDate":"1972-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88221677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1972-11-01DOI: 10.1088/0305-4470/5/11/004
R. Phythian
A variational method, similar to the Frenkel variational method of quantum mechanics, is derived for the time development of phase functions of a system. It is shown how this method may be used to obtain approximations for quantities of interest such as the density autocorrelation function of a fluid in equilibrium.
{"title":"A variational method in statistical mechanics","authors":"R. Phythian","doi":"10.1088/0305-4470/5/11/004","DOIUrl":"https://doi.org/10.1088/0305-4470/5/11/004","url":null,"abstract":"A variational method, similar to the Frenkel variational method of quantum mechanics, is derived for the time development of phase functions of a system. It is shown how this method may be used to obtain approximations for quantities of interest such as the density autocorrelation function of a fluid in equilibrium.","PeriodicalId":54612,"journal":{"name":"Physics-A Journal of General and Applied Physics","volume":"17 1","pages":"1566-1572"},"PeriodicalIF":0.0,"publicationDate":"1972-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88273185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1972-11-01DOI: 10.1088/0305-4470/5/11/006
J. Askne
Waves in a general dispersive medium represented by a quadratic or bilinear Lagrangian are quantized. A phenomenological method is used leading to medium excitations in terms of quasiparticles (bosons) which are photon-like, phonon-like etc. The possibility for negative energy excitations is considered and interactions between different wave types studied. The simplicity of the analysis is demonstrated by an analysis of nonlinear interactions in a multistream medium of plasmons.
{"title":"Quantization of waves in dispersive media with application to nonlinear interactions of plasmons","authors":"J. Askne","doi":"10.1088/0305-4470/5/11/006","DOIUrl":"https://doi.org/10.1088/0305-4470/5/11/006","url":null,"abstract":"Waves in a general dispersive medium represented by a quadratic or bilinear Lagrangian are quantized. A phenomenological method is used leading to medium excitations in terms of quasiparticles (bosons) which are photon-like, phonon-like etc. The possibility for negative energy excitations is considered and interactions between different wave types studied. The simplicity of the analysis is demonstrated by an analysis of nonlinear interactions in a multistream medium of plasmons.","PeriodicalId":54612,"journal":{"name":"Physics-A Journal of General and Applied Physics","volume":"105 1","pages":"1578-1586"},"PeriodicalIF":0.0,"publicationDate":"1972-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80591357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1972-11-01DOI: 10.1088/0305-4470/5/11/007
S. Swain
The problem of a single two level atom in its excited state, placed in a cavity in which no photons are present initially, and interacting with N modes of the electromagnetic field is solved exactly in the electric dipole, rotating wave approximation. Expressions for the energy eigenvalues and eigenvectors are derived, and an exact representation for the time dependent wavefunction of the system is given. These quantities are evaluated analytically for N=1,2 and 3, and the time dependent properties of the system for these values of N are investigated and discussed.
{"title":"An exact analysis of spontaneous emission by a single two level atom in the rotating wave approximation II. Numerical results","authors":"S. Swain","doi":"10.1088/0305-4470/5/11/007","DOIUrl":"https://doi.org/10.1088/0305-4470/5/11/007","url":null,"abstract":"The problem of a single two level atom in its excited state, placed in a cavity in which no photons are present initially, and interacting with N modes of the electromagnetic field is solved exactly in the electric dipole, rotating wave approximation. Expressions for the energy eigenvalues and eigenvectors are derived, and an exact representation for the time dependent wavefunction of the system is given. These quantities are evaluated analytically for N=1,2 and 3, and the time dependent properties of the system for these values of N are investigated and discussed.","PeriodicalId":54612,"journal":{"name":"Physics-A Journal of General and Applied Physics","volume":"19 1","pages":"1587-1600"},"PeriodicalIF":0.0,"publicationDate":"1972-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87226251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1972-11-01DOI: 10.1088/0305-4470/5/11/010
F. El-Bedewi, M. Shalaby
The 28Si(d,p)29Si reaction has been studied at Ed=10 MeV with a multigap magnetic spectrograph which can record 24 spectra at angles ranging from 5 degrees to 175 degrees . Eighty two proton groups have been identified as belonging to the 28Si(d,p) reaction covering excitation energies in 29Si up to 9-676 MeV. Angular distribution measurements on 61 proton groups corresponding to levels up to 9.154 MeV have been carried out and those exhibiting stripping patterns have been analysed. Spectroscopic factors for bound states have been derived using the finite range DWBA method with nonlocal correlation FRNL.
{"title":"Study of energy levels of 29Si via deuteron stripping","authors":"F. El-Bedewi, M. Shalaby","doi":"10.1088/0305-4470/5/11/010","DOIUrl":"https://doi.org/10.1088/0305-4470/5/11/010","url":null,"abstract":"The 28Si(d,p)29Si reaction has been studied at Ed=10 MeV with a multigap magnetic spectrograph which can record 24 spectra at angles ranging from 5 degrees to 175 degrees . Eighty two proton groups have been identified as belonging to the 28Si(d,p) reaction covering excitation energies in 29Si up to 9-676 MeV. Angular distribution measurements on 61 proton groups corresponding to levels up to 9.154 MeV have been carried out and those exhibiting stripping patterns have been analysed. Spectroscopic factors for bound states have been derived using the finite range DWBA method with nonlocal correlation FRNL.","PeriodicalId":54612,"journal":{"name":"Physics-A Journal of General and Applied Physics","volume":"472 1","pages":"1624-1638"},"PeriodicalIF":0.0,"publicationDate":"1972-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79922354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：