Geodesic
On an approximate analytical method for solving the Schr\"odinger equation with the Gaussian potential
Problemy fiziki, matematiki i tehniki, no. 4 (2019), pp. 7-10.

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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. 
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Yu. A. Grishechkin; A. V. Pavlenko; V. N. Kapshai. On an approximate analytical method for solving the Schr\"odinger 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.