Papers by G Bruce Mainland
Nuovo Cimento a Nucl Part F, 1984
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
Quantum Physics, 2019
So far only properties such as the structure and spectra of quantum physical systems have been di... more So far only properties such as the structure and spectra of quantum physical systems have been discussed, properties for which time development is irrelevant and can thus be ignored. In this chapter properties will be discussed that can be understood only by taking into account time development.
Quantum Physics, 2019
The story of quantum physics began in 1900 when Max Planck discovered by the thermodynamical meth... more The story of quantum physics began in 1900 when Max Planck discovered by the thermodynamical methods the improvement of the Wien’s law of energy distribution for blackbody radiation and then formulated the microscopic derivation of his equation in terms of oscillators within the cavity of a blackbody.
Quantum Physics, 2019
The structure of quantum systems is studied by “looking at them” with light or with other quantum... more The structure of quantum systems is studied by “looking at them” with light or with other quantum systems such as electrons that are usually more fundamental and have less structure than the physical system being investigated. If a quantum particle has no internal structure and is a point object, it is fundamental and is called an elementary particle.
Lettere al Nuovo Cimento, 1982
SummaryWe investigate a charge magnetic-dipole model originally suggested by Barut to qualitative... more SummaryWe investigate a charge magnetic-dipole model originally suggested by Barut to qualitatively explain the lepton mass spectrum. In contrast to the encouraging results he finds using Bohr-Sommerfeld quantization, we find that successive energy levels do not increase rapidly enough to account for the observed lepton masses. None of the bound states are stable, and the states with lowest energies have unacceptably large angular moments.
Journal of Mathematical Physics, 1988
Zero four-momentum, helicity eigenstates of the Bethe--Salpeter equation are found for a composit... more Zero four-momentum, helicity eigenstates of the Bethe--Salpeter equation are found for a composite system consisting of a charged, spin-0 constituent and a charged, spin- 1/2 constituent bound by minimal electrodynamics. The form of the Bethe--Salpeter equation used to describe the bound state includes the contributions from both single photon exchange (ladder approximation) and the ''seagull'' diagram. Attention is restricted to zero orbital angular momentum states since these appear to be the most interesting physically.
Journal of Mathematical Physics, 1991
Differential equations for an orthogonal transformation that separates the Bethe–Salpeter equatio... more Differential equations for an orthogonal transformation that separates the Bethe–Salpeter equation for the Wick–Cutkosky model will be derived and then solved. Although the transformation in which the Wick–Cutkosky model separates is already known, the systematic procedure presented for deriving the transformation may be useful for determining orthogonal transformations that would permit the separation of other Bethe–Salpeter equations.
International Journal of Theoretical Physics, 1984
We investigate bound states of a composite system consisting of a charged particle orbiting a neu... more We investigate bound states of a composite system consisting of a charged particle orbiting a neutral, stationary magnetic dipole. We find all bound states are metastable and none exist with angular momentum less than eleven. Our calculation is performed in two space dimensions.
Fortschritte der Physik, 1970
Few-Body Systems, 2003
The characteristic of bound-state, Bethe-Salpeter equations that makes them so difficult to solve... more The characteristic of bound-state, Bethe-Salpeter equations that makes them so difficult to solve numerically can be overcome, in some if not many cases, by expanding solutions in terms of basis functions that obey the boundary conditions that are satisfied by the solutions. The utility of such basis functions is demonstrated by calculating the zero-energy, bound-state solutions of a spin-0 boson and a spin-1 2 fermion with unequal masses. The constituents interact via scalar electrodynamics and are described by the Bethe-Salpeter equation in the ladder approximation. Although the Bethe-Salpeter equation that is solved is separable in the zero-energy limit, the feature that typically prevents solutions from being obtained numerically is still present. A technique for calculating boundary conditions, which is readily generalized to other Bethe-Salpeter equations, is discussed in detail.
Few-Body Systems, 1995
. We discuss a numerical technique for solving four-dimensional, relativistic, bound-state, two... more . We discuss a numerical technique for solving four-dimensional, relativistic, bound-state, two-body equations that have not been completely separated. The angular variables are first separated what is always possible for a rotationally invariant system. The resulting partially separated equation is, in general, a set of coupled integral or partial differential equations in two variables that is solved numerically by expressing the solutions in terms of B-splines. We demonstrate the efficacy of the method by solving the partially separated Bethe-Salpeter equation for the equal-mass, Wick-Cutkosky model in the ladder approximation.
Czechoslovak Journal of Physics, 2005
Solutions are obtained to the Bethe-Salpeter equation describing bound states of two massive scal... more Solutions are obtained to the Bethe-Salpeter equation describing bound states of two massive scalars interacting via the exchange of a third, massive scalar. Covariance of the equation implies that the interaction is retarded, and in part because the energy appears more than once in the equation, a Hamiltonian for the bound state does not exist. Thus in contrast to the Schrodinger equation, the Bethe-Salpeter equation is solved by specifying the energy and solving for the coupling constant as an eigenvalue. Although the Bethe-Salpeter equation is derived from a Lagrangian with real coupling constants, depending on the value of the energy and the masses of the scalars, some values of the coupling constant that satisfy the Bethe-Salpeter equation are complex and always occur in conjugate pairs. The unexpected existence of solutions with real energy and a complex coupling constant raises the possibility that there are also resonance solutions with real values of the coupling constant and complex energy.
American Journal of Physics, 1989
Gamow vectors are generalized eigenvectors of the Hamiltonian with complex eigenvalues that descr... more Gamow vectors are generalized eigenvectors of the Hamiltonian with complex eigenvalues that describe exponentially decaying (or growing) states. The energy wavefunctions corresponding to Gamow vectors have a pole immediately below (or above) the real axis in the complex energy plane. Although complex energy values were introduced more than half a century ago for the theory of alpha decay, they have
Journal of Computational Physics, 2004
The difficulties that typically prevent numerical solutions from being obtained to finite-energy,... more The difficulties that typically prevent numerical solutions from being obtained to finite-energy, two-body, bound-state Bethe-Salpeter equations can often be overcome by expanding solutions in terms of basis functions that obey the boundary conditions. The method discussed here for solving the Bethe-Salpeter equation requires only that the equation can be Wick rotated and that the two angular variables associated with rotations in three-dimensional space can be separated, properties that are possessed by many Bethe-Salpeter equations including all two-body, bound-state Bethe-Salpeter equations in the ladder approximation. The efficacy of the method is demonstrated by calculating finite-energy solutions to the partially-separated Bethe-Salpeter equation describing the Wick-Cutkosky model when the constituents do not have equal masses.
Bound-state solutions are obtained numerically in the instantaneous approximation for a spin-0 an... more Bound-state solutions are obtained numerically in the instantaneous approximation for a spin-0 and spin-1/2 constituent that interact via minimal electrodynamics. To solve the integral equations in momentum space, a method is developed for integrating over the logarithmic singularity in kernels, making it possible to use basis functions that essentially automatically satisfy the boundary conditions. For bound-state solutions that decrease rapidly at small and large values of momentum, accurate solutions are obtained with significantly fewer basis functions when the solution is expanded in terms of these more general basis functions. The presence of a derivative coupling in single-photon exchange complicates the construction of the Bethe-Salpeter equation in the instantaneous approximation and, in the nonrelativistic limit, gives rise to an additional electrostatic potential term that is second order in the coupling constant and decreases as the square of the distance between constit...
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Papers by G Bruce Mainland