Using the coordinate transformation method, we solve the one-dimensional Schrodinger equation with position-dependent mass. The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the sy...Using the coordinate transformation method, we solve the one-dimensional Schrodinger equation with position-dependent mass. The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the systems are given. The eigenfunctions can be expressed in terms of the Jacobi, Hermite, and generalized Laguerre polynomials. All potentials for these solvable systems have an extra term Vm, which is produced from the dependence of mass on the position, compared with those for the systems of constant mass. The properties of Vm for several mass functions are discussed.展开更多
The entity and symbolic fraction comparison tasks separating identification and semantic access stages based on event-related potential technology were used to investigate neural differences between fraction and decim...The entity and symbolic fraction comparison tasks separating identification and semantic access stages based on event-related potential technology were used to investigate neural differences between fraction and decimal strategies in magnitude processing of nonsymbolic entities and symbolic numbers.The experimental results show that continuous entities elicit stronger left-lateralized anterior N2 in decimals,while discretized ones elicit more significant right-lateralized posterior N2 in fractions during the identification stage.On the other hand,decimals elicit stronger N2 over the left-lateralized fronto-central sites while fractions elicit the more profound P2 over the right-lateralized fronto-central sites and N2 at biparietal regions during the semantic access stage.Hence,for nonsymbolic entity processing,alignments of decimals and continuous entities activate the phonological network,while alignments of fractions and discretized entities trigger the visuospatial regions.For symbolic numbers processing,exact strategies with rote arithmetic retrieval in verbal format are used in decimal processing,while approximate strategies with complex magnitude processing in a visuospatial format are used in fraction processing.展开更多
基金The project supported by National Natural Science Foundation of China for 0utstanding Young Scientists under Grant No. 10125521, the Doctoral Fund of the Ministry of Education under Grant No. 20010284036, the State Key Basic Research Development Program of China under Grant No. G2000077400, the Chinese Academy of Sciences Knowledge Innovation Project under Grant No. KJCX2-SW-N02, and National Natural Science Foundation of China under Grant No. 60371013
文摘Using the coordinate transformation method, we solve the one-dimensional Schrodinger equation with position-dependent mass. The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the systems are given. The eigenfunctions can be expressed in terms of the Jacobi, Hermite, and generalized Laguerre polynomials. All potentials for these solvable systems have an extra term Vm, which is produced from the dependence of mass on the position, compared with those for the systems of constant mass. The properties of Vm for several mass functions are discussed.
基金The National Natural Science Foundation of China(No.62077013,61773114)the Jiangsu Provincial Innovation Project for Scientific Research of Graduate Students in Universities(No.KYCX17_0160).
文摘The entity and symbolic fraction comparison tasks separating identification and semantic access stages based on event-related potential technology were used to investigate neural differences between fraction and decimal strategies in magnitude processing of nonsymbolic entities and symbolic numbers.The experimental results show that continuous entities elicit stronger left-lateralized anterior N2 in decimals,while discretized ones elicit more significant right-lateralized posterior N2 in fractions during the identification stage.On the other hand,decimals elicit stronger N2 over the left-lateralized fronto-central sites while fractions elicit the more profound P2 over the right-lateralized fronto-central sites and N2 at biparietal regions during the semantic access stage.Hence,for nonsymbolic entity processing,alignments of decimals and continuous entities activate the phonological network,while alignments of fractions and discretized entities trigger the visuospatial regions.For symbolic numbers processing,exact strategies with rote arithmetic retrieval in verbal format are used in decimal processing,while approximate strategies with complex magnitude processing in a visuospatial format are used in fraction processing.
