This work presents results of the different parameters which characterize the nonrelativistic Hamilton operator for the helium atoms allowing us to solve the Schrödinger equation. The total energy is decomposed i...This work presents results of the different parameters which characterize the nonrelativistic Hamilton operator for the helium atoms allowing us to solve the Schrödinger equation. The total energy is decomposed into three terms allowing to separate the kinetic energy, the electrons-nucleus interaction energy and the electron-electron interaction energy of the (2s<sup>2</sup>, 3s<sup>2</sup> and 4s<sup>2</sup>) <sup>1</sup>S<sup>e</sup>, (2p<sup>2</sup>, 3p<sup>2</sup> and 4p<sup>2</sup>) <sup>1</sup>D<sup>e</sup> and (3d<sup>2</sup> and 4d<sup>2</sup>) <sup>1</sup>G<sup>e</sup> resonance singlet states of the helium isoelectronic sequences. The states have been defined by using special forms of the Hylleraas type wave functions. The calculations have been carried out in the framework of the variational method using configuration interaction basis states with a real Hamiltonian. The agreement of the energy value of other states between the present theoretical values available in the literature is excellent. But as for the comparison of the kinetic energies, the electrons-nucleus energies interaction and the electron-electron interaction energies, we note a slight difference with the theoretical values common in literature.展开更多
In this work, the effects of quantum confinement on the ground state energy of a correlated electron-hole pair in a spherical and in a disc-like quantum dot have been investigated as a function of quantum dot size. Un...In this work, the effects of quantum confinement on the ground state energy of a correlated electron-hole pair in a spherical and in a disc-like quantum dot have been investigated as a function of quantum dot size. Under parabolic confinement potential and within effective mass approximation Ritz＇s variational method is applied to Hylleraas-like trial wavefunction. An efficient method for reducing the main effort of the calculation of terms like τekh exp （-λτeh） is introduced. The main contribution of the present work is the introduction of integral transforms which provide the calculation of expectation value of energy and the related matrix elements to be done analytically over single-particle coordinates instead of Hvlleraas coordinates.展开更多
In this work, we propose an efficient method of reducing the computational effort of variational calculation with a Hylleraas-like trial wavefunction. The method consists of introducing integral transforms for the ter...In this work, we propose an efficient method of reducing the computational effort of variational calculation with a Hylleraas-like trial wavefunction. The method consists of introducing integral transforms for the terms as r12^κ exp （-λτ12） which provide the calculation of the expectation value of energy and the relevant matrix elements to be done analytically over single-electron coordinates instead of Hylleraas coordinates. We have used this method to calculate the ground state energy of a two-electron system in a spherical dot and a disk-like quantum dot separately. Under parabolic confinement potential and within effective mass approximation size and shape effects of quantum dots on the ground state energy of two electrons have been investigated. The calculation shows that our results even with a small number of basis states are in good agreement with previous theoretical results.展开更多
Precise energy eigenvalues of metastable bound doubly excited 1,3Fe states originating from 2 pnf(n=4–6)configuration of helium-like ions(Z=2–4)under weakly coupled plasma(WCP)environment have been estimated within ...Precise energy eigenvalues of metastable bound doubly excited 1,3Fe states originating from 2 pnf(n=4–6)configuration of helium-like ions(Z=2–4)under weakly coupled plasma(WCP)environment have been estimated within the framework of Ritz variational method.The wavefunction is expanded in explicitly correlated Hylleraas type basis set.The screened Coulomb potential is consideredas mimic the WCP environment.The atomic systems tend towards gradual instability and the number of excited metastable bound states reduces with increasing plasma strength.The wavelengths corresponding to 2 pnf(1,3F^e)→2 pnf(1,3Do)(n=4–6;n′=3–6)transitions occurring between doubly excited states of plasma embedded two-electron ions are also reported.展开更多
The relativistic study of spinless particles under a special case of equal scalar and vector generalized Hylleraas potential with position dependent mass has been studied. The energy eigenvalues and the corresponding ...The relativistic study of spinless particles under a special case of equal scalar and vector generalized Hylleraas potential with position dependent mass has been studied. The energy eigenvalues and the corresponding wave functions expressed in terms ofa Jacobi polynomial are obtained using the parametric generalization of NU （Nikiforo-Uvarov） method. In obtaining the solutions for this system, we have used an approximation scheme to evaluate the centrifugal term （potential barrier）. To test the accuracy of the result, we compared the approximation scheme with the centrifugal term and the result shows a good agreement with the centrifugal term for a short-range potential. The results obtained in this work would have many applications in semiconductor quantum well structures, quantum dots, quantum liquids. Under limiting cases, the results could be used to study the binding energy and interaction of some diatomic molecules which is of great applications in nuclear physics, atomic and molecular physics and other related areas. We have also discussed few special cases of generalized Hylleraas potential such as Rosen-Morse, Woods-Saxon and Hulthen potentials.展开更多
In this study, the energy for the ground state of helium and a few helium-like ions （Z=1-6） is computed variationally by using a Hylleraas-like wavefunction. A four-parameters wavefunction, satisfying boundary condi...In this study, the energy for the ground state of helium and a few helium-like ions （Z=1-6） is computed variationally by using a Hylleraas-like wavefunction. A four-parameters wavefunction, satisfying boundary conditions for coalescence points, is combined with a Hylleraas-like basis set which explicitly incorporates r12 interelectronic distance. The main contribution of this work is the introduction of modified correlation terms leading to the definition of integral transforms which provide the calculation of expectation value of energy to be done analytically over single-particle coordinates instead of Hylleraas coordinates.展开更多
We study the d-dimensional Schrdinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov-Uvarov method.We obtain energy eigenvalues and the corresponding...We study the d-dimensional Schrdinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov-Uvarov method.We obtain energy eigenvalues and the corresponding wave function expressed in terms of a Jacobi polynomial.We also discuss two special cases of this potential comprised of the Hulthen potential and the Rosen-Morse potential in three dimensions.Numerical results are also computed for the energy spectrum and the potentials.展开更多
文摘This work presents results of the different parameters which characterize the nonrelativistic Hamilton operator for the helium atoms allowing us to solve the Schrödinger equation. The total energy is decomposed into three terms allowing to separate the kinetic energy, the electrons-nucleus interaction energy and the electron-electron interaction energy of the (2s<sup>2</sup>, 3s<sup>2</sup> and 4s<sup>2</sup>) <sup>1</sup>S<sup>e</sup>, (2p<sup>2</sup>, 3p<sup>2</sup> and 4p<sup>2</sup>) <sup>1</sup>D<sup>e</sup> and (3d<sup>2</sup> and 4d<sup>2</sup>) <sup>1</sup>G<sup>e</sup> resonance singlet states of the helium isoelectronic sequences. The states have been defined by using special forms of the Hylleraas type wave functions. The calculations have been carried out in the framework of the variational method using configuration interaction basis states with a real Hamiltonian. The agreement of the energy value of other states between the present theoretical values available in the literature is excellent. But as for the comparison of the kinetic energies, the electrons-nucleus energies interaction and the electron-electron interaction energies, we note a slight difference with the theoretical values common in literature.
文摘In this work, the effects of quantum confinement on the ground state energy of a correlated electron-hole pair in a spherical and in a disc-like quantum dot have been investigated as a function of quantum dot size. Under parabolic confinement potential and within effective mass approximation Ritz＇s variational method is applied to Hylleraas-like trial wavefunction. An efficient method for reducing the main effort of the calculation of terms like τekh exp （-λτeh） is introduced. The main contribution of the present work is the introduction of integral transforms which provide the calculation of expectation value of energy and the related matrix elements to be done analytically over single-particle coordinates instead of Hvlleraas coordinates.
基金supported by the Cumhuriyet University,National MOVPE Crystal Growth and Characterization Laboratory,Turkey,DPT-K 120,TUBITAK (Grant Nos TBAG 105T492,TBAG 107T012,and TBAG-108T015)
文摘In this work, we propose an efficient method of reducing the computational effort of variational calculation with a Hylleraas-like trial wavefunction. The method consists of introducing integral transforms for the terms as r12^κ exp （-λτ12） which provide the calculation of the expectation value of energy and the relevant matrix elements to be done analytically over single-electron coordinates instead of Hylleraas coordinates. We have used this method to calculate the ground state energy of a two-electron system in a spherical dot and a disk-like quantum dot separately. Under parabolic confinement potential and within effective mass approximation size and shape effects of quantum dots on the ground state energy of two electrons have been investigated. The calculation shows that our results even with a small number of basis states are in good agreement with previous theoretical results.
基金Supported under Grant No. EMR/2017/000737 from DST-SERB, Govt. of India, Grant No. 23(Sanc.)/ST/P/S&T/16G-35/2017 from DHESTB, Govt. of West Bengal, Indiaby the DHESTB,Govt.of West Bengal,India under Grant No.249(Sanc.)/ST/P/S&T/16G-26/2017
文摘Precise energy eigenvalues of metastable bound doubly excited 1,3Fe states originating from 2 pnf(n=4–6)configuration of helium-like ions(Z=2–4)under weakly coupled plasma(WCP)environment have been estimated within the framework of Ritz variational method.The wavefunction is expanded in explicitly correlated Hylleraas type basis set.The screened Coulomb potential is consideredas mimic the WCP environment.The atomic systems tend towards gradual instability and the number of excited metastable bound states reduces with increasing plasma strength.The wavelengths corresponding to 2 pnf(1,3F^e)→2 pnf(1,3Do)(n=4–6;n′=3–6)transitions occurring between doubly excited states of plasma embedded two-electron ions are also reported.
文摘The relativistic study of spinless particles under a special case of equal scalar and vector generalized Hylleraas potential with position dependent mass has been studied. The energy eigenvalues and the corresponding wave functions expressed in terms ofa Jacobi polynomial are obtained using the parametric generalization of NU （Nikiforo-Uvarov） method. In obtaining the solutions for this system, we have used an approximation scheme to evaluate the centrifugal term （potential barrier）. To test the accuracy of the result, we compared the approximation scheme with the centrifugal term and the result shows a good agreement with the centrifugal term for a short-range potential. The results obtained in this work would have many applications in semiconductor quantum well structures, quantum dots, quantum liquids. Under limiting cases, the results could be used to study the binding energy and interaction of some diatomic molecules which is of great applications in nuclear physics, atomic and molecular physics and other related areas. We have also discussed few special cases of generalized Hylleraas potential such as Rosen-Morse, Woods-Saxon and Hulthen potentials.
基金Project supported by the Cumhuriyet University National MOVPE Crystal Growth and Characterization Laboratory,DPT-K120,TUBITAK (Grant Nos TBAG 105T492,TBAG 107T012,and TBAG-108T015)
文摘In this study, the energy for the ground state of helium and a few helium-like ions （Z=1-6） is computed variationally by using a Hylleraas-like wavefunction. A four-parameters wavefunction, satisfying boundary conditions for coalescence points, is combined with a Hylleraas-like basis set which explicitly incorporates r12 interelectronic distance. The main contribution of this work is the introduction of modified correlation terms leading to the definition of integral transforms which provide the calculation of expectation value of energy to be done analytically over single-particle coordinates instead of Hylleraas coordinates.
文摘We study the d-dimensional Schrdinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov-Uvarov method.We obtain energy eigenvalues and the corresponding wave function expressed in terms of a Jacobi polynomial.We also discuss two special cases of this potential comprised of the Hulthen potential and the Rosen-Morse potential in three dimensions.Numerical results are also computed for the energy spectrum and the potentials.
