We discuss the equivalent form of the Ldvy-Leblond equation such that the nilpotent matrices are two-dimensional. We show that this equation can be obtained in the non-relativistic limit of the （2＋1）-dimensional Di...We discuss the equivalent form of the Ldvy-Leblond equation such that the nilpotent matrices are two-dimensional. We show that this equation can be obtained in the non-relativistic limit of the （2＋1）-dimensional Dirac equation. Phrthermore, we analyze the case with four-dimensional matrices, propose a Hamiltonian for the equation in （3＋1） dimensions, and solve it for a Coulomb potential The quantized energy levels for the hydrogen atom are obtained, and the result is consistent with the non-relativistic quantum mechanics.展开更多
The photostimulated reaction of halonaphthalene with a series of carbanions derived from, propionic acid derivatives in liquid ammonia led to the naphthylation at a-carbon of the carbanions in an isolated yield rangin...The photostimulated reaction of halonaphthalene with a series of carbanions derived from, propionic acid derivatives in liquid ammonia led to the naphthylation at a-carbon of the carbanions in an isolated yield ranging from 25％ to 86％.In all cases,the dehalonaphthalenes were found to, be by-products and the reaction was inhibited by p-dinitrobenzere.An electron transfer from the carbanion to the halonaphthalene followed by ejection of halogen led to naphtbyl radical,as predicted by comparing the LUMOs of the carbanions and the halonaphthalenes,was involved in the process. Absence of the alkylnaphthalene and 1,2-dinaphthylalkane in the products indicates the smooth electron transfer between(Naph-Nu)^+ and Naph-X.C-vs.O-naphthylation is fully addressed in terms of MNDO calculations and acid-base principle.展开更多
文摘We discuss the equivalent form of the Ldvy-Leblond equation such that the nilpotent matrices are two-dimensional. We show that this equation can be obtained in the non-relativistic limit of the （2＋1）-dimensional Dirac equation. Phrthermore, we analyze the case with four-dimensional matrices, propose a Hamiltonian for the equation in （3＋1） dimensions, and solve it for a Coulomb potential The quantized energy levels for the hydrogen atom are obtained, and the result is consistent with the non-relativistic quantum mechanics.
基金Work supported by the National Natural Science Foundation of China.
文摘The photostimulated reaction of halonaphthalene with a series of carbanions derived from, propionic acid derivatives in liquid ammonia led to the naphthylation at a-carbon of the carbanions in an isolated yield ranging from 25％ to 86％.In all cases,the dehalonaphthalenes were found to, be by-products and the reaction was inhibited by p-dinitrobenzere.An electron transfer from the carbanion to the halonaphthalene followed by ejection of halogen led to naphtbyl radical,as predicted by comparing the LUMOs of the carbanions and the halonaphthalenes,was involved in the process. Absence of the alkylnaphthalene and 1,2-dinaphthylalkane in the products indicates the smooth electron transfer between(Naph-Nu)^+ and Naph-X.C-vs.O-naphthylation is fully addressed in terms of MNDO calculations and acid-base principle.
