On an approximate analytical method for solving the Schrödinger equation with the Gaussian potential
Problemy fiziki, matematiki i tehniki, no. 4 (2019), pp. 7-10 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The approximate analytical method for solving the Schrödinger equation with the Gaussian potential is proposed. The essence of the method is to represent the wave function as a superposition of wave functions of exact solving problem Also, in order to control the accuracy, the problem was solved numerically in the momentum representation.
Keywords: Schrödinger equation, integral equation, wave function, Gaussian potential, harmonic oscillator.
@article{PFMT_2019_4_a0,
     author = {Yu. A. Grishechkin and A. V. Pavlenko and V. N. Kapshai},
     title = {On an approximate analytical method for solving the {Schr\"odinger} equation with the {Gaussian} potential},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {7--10},
     year = {2019},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2019_4_a0/}
}
TY  - JOUR
AU  - Yu. A. Grishechkin
AU  - A. V. Pavlenko
AU  - V. N. Kapshai
TI  - On an approximate analytical method for solving the Schrödinger equation with the Gaussian potential
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2019
SP  - 7
EP  - 10
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/PFMT_2019_4_a0/
LA  - ru
ID  - PFMT_2019_4_a0
ER  - 
%0 Journal Article
%A Yu. A. Grishechkin
%A A. V. Pavlenko
%A V. N. Kapshai
%T On an approximate analytical method for solving the Schrödinger equation with the Gaussian potential
%J Problemy fiziki, matematiki i tehniki
%D 2019
%P 7-10
%N 4
%U http://geodesic.mathdoc.fr/item/PFMT_2019_4_a0/
%G ru
%F PFMT_2019_4_a0
Yu. A. Grishechkin; A. V. Pavlenko; V. N. Kapshai. On an approximate analytical method for solving the Schrödinger equation with the Gaussian potential. Problemy fiziki, matematiki i tehniki, no. 4 (2019), pp. 7-10. http://geodesic.mathdoc.fr/item/PFMT_2019_4_a0/

[1] G. Stephenson, “Eigenvalues of the Schrodinger equation with a Gaussian potential”, J. Phys. A: Math Gen., 10 (1977), L229–L232 | DOI | MR | Zbl

[2] C.S. Lai, “On the Schrodinger equation for the Gaussian potential $-A\exp(-\lambda r^2)$”, J. Phys. A: Math Gen., 16 (1983), L181–L185 | DOI | MR | Zbl

[3] R.E. Crandale, “Fast eigenvalue algorithm for central potentials”, J. Phys. A: Math Gen., 16 (1983), L395–L399 | DOI | MR

[4] A. Chatterjee, “$1/N$ expansion for Gaussian potential”, J. Phys. A: Math. Gen., 18 (1985), 2403–2408 | DOI | MR

[5] S.S. Gomez, R.H. Romero, “Few-electron semiconductor quantum dots with Gaussian confinement”, Central Eur. J. Phys., 7 (2009), 12–21

[6] K. Koksal, “A simple analytical expression for bound state energies for an attractive Gaussian confining potential”, Phys. Scr., 86 (2012), 035006 | DOI | Zbl

[7] A.S. Davydov, Kvantovaya mekhanika, 3-e izd., BKhV-Peterburg, SPb., 2011, 699 pp.

[8] Z. Flyugge, Zadachi po kvantovoi mekhaniki, v 2 t., v. 1, 3-izd., LKI, M., 2010, 344 pp.

[9] G. Arfken, Matematicheskie metody v fizike, Atomizdat, M., 1970, 712 pp.

[10] I.S. Gradshtein, I.M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvodnykh, 4-e izd., M., 1963, 1108 pp.

[11] N.N. Kalitkin, Chislennye metody, BKhV-Peterburg, Sankt-Peterburg, 2011, 592 pp.