FK OPERATOR FOR TWO-DIMENSIONAL MOLECULAR HYDROGEN ION H2+ IN A UNIFORM ELECTRIC FIELD
Main Article Content
Abstract
The article shows how the Schrödinger equation of two-dimensional molecular hydrogen ion in a uniform electric field was solved by using the FK operator method. Matrix elements of Hamiltonian are obtained, which allows calculating numerical solutions (wave functions and energy) of the problem.
Keywords
two-dimensional molecular hydrogen ion, FK operator method, matrix elements, numerical solution
Article Details
References
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Hoang-Do, N. T., Pham, D. L., & Le, V. H. (2013). Exact numerical solutions of the Schrodinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength. Physica B: Condensed Matter, 423, 31-37. https://doi.org/10.1016/j.physb.2013.04.040
Ivanov, M. V., & Schinke, R. (2004). Two-dimensional analogs of the + ion in stationary electric fields. Physical Review B - Condensed Matter and Materials Physics, 69(16), 1-9. https://doi.org/10.1103/PhysRevB.69.165308
Karr, J. P., Hilico, L., Koelemeij, J. C. J., & Korobov, V. I. (2016). Hydrogen molecular ions for improved determination of fundamental constants. Physical Review A, 94(5), 6-10. https://doi.org/10.1103/PhysRevA.94.050501
Korobov, V. I., Danev, P., Bakalov, D., & Schiller, S. (2018). Laser-stimulated electric quadrupole transitions in the molecular hydrogen ion . Physical Review A, 97(3), 032505–032508. https://doi.org/10.1103/PhysRevA.97.032505
Korobov, Vladimir I., Koelemeij, J. C. J., Hilico, L., & Karr, J. P. (2016). Theoretical Hyperfine Structure of the Molecular Hydrogen Ion at the 1 ppm Level. Physical Review Letters, 116(5), 1-5. https://doi.org/10.1103/PhysRevLett.116.053003
Nguyen, Phuong Duy Anh, Hoang, Do Ngoc Tram (2018). Matrix elements for two-dimensional heli atom. Ho Chi Minh City Unviversity of Education Journal of Science (Special Issue: Natural Sciences and Technology, 15(9), 22-34.
Patil, S. H. (2003). Hydrogen molecular ion and molecule in two dimensions. Journal of Chemical Physics, 118(5), 2197-2205. https://doi.org/10.1063/1.1531103
Bates, D. R., Ledsham, K., & Stewart, A. L. (2006). Wave Functions of the Hydrogen Molecular Ion. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 246(911), 215-240. https://doi.org/10.1098/rsta.1953.0014
Du, L. L., Wang, G. L., Li, P. C., Zhou, X. X., & Zhao, Z. X. (2018). Interference effect in low-order harmonic generation of in intense laser fields. Physical Review A, 97(2), 023404-023406. https://doi.org/10.1103/PhysRevA.97.023404
Hoang-Do, N. T., Pham, D. L., & Le, V. H. (2013). Exact numerical solutions of the Schrodinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength. Physica B: Condensed Matter, 423, 31-37. https://doi.org/10.1016/j.physb.2013.04.040
Ivanov, M. V., & Schinke, R. (2004). Two-dimensional analogs of the + ion in stationary electric fields. Physical Review B - Condensed Matter and Materials Physics, 69(16), 1-9. https://doi.org/10.1103/PhysRevB.69.165308
Karr, J. P., Hilico, L., Koelemeij, J. C. J., & Korobov, V. I. (2016). Hydrogen molecular ions for improved determination of fundamental constants. Physical Review A, 94(5), 6-10. https://doi.org/10.1103/PhysRevA.94.050501
Korobov, V. I., Danev, P., Bakalov, D., & Schiller, S. (2018). Laser-stimulated electric quadrupole transitions in the molecular hydrogen ion . Physical Review A, 97(3), 032505–032508. https://doi.org/10.1103/PhysRevA.97.032505
Korobov, Vladimir I., Koelemeij, J. C. J., Hilico, L., & Karr, J. P. (2016). Theoretical Hyperfine Structure of the Molecular Hydrogen Ion at the 1 ppm Level. Physical Review Letters, 116(5), 1-5. https://doi.org/10.1103/PhysRevLett.116.053003
Nguyen, Phuong Duy Anh, Hoang, Do Ngoc Tram (2018). Matrix elements for two-dimensional heli atom. Ho Chi Minh City Unviversity of Education Journal of Science (Special Issue: Natural Sciences and Technology, 15(9), 22-34.
Patil, S. H. (2003). Hydrogen molecular ion and molecule in two dimensions. Journal of Chemical Physics, 118(5), 2197-2205. https://doi.org/10.1063/1.1531103