Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials
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The computer – assisted solution of the one – dimensional Schrödinger equation taking into account tunneling effects

I.N. Belyaeva1, I.K. Kirichenko2, O.D. Ptashnyi3, N.N. Chekanova4, N.A. Chekanov1, T.A. Yarkho3

1Belgorod National Research University, Belgorod, Russia

2National University of Civil Defence of Ukraine, Kharkiv, Ukraine

3Kharkiv National Automobile and Highway University, Kharkiv, Ukraine

4Kharkiv Educational and Research Institute of the Higher Educational Institution «University of Banking», Kharkiv, Ukraine

DOI: 10.26456/pcascnn/2019.11.283

Abstract: The general scheme of the method of integration of the second order ordinary differential equations with regular singular points is outlined. The algorithm of finding a general solution of the second order differential equation with regular singular points is given. The Schr dinger equation for anharmonic oscillator with the potential of the fourth, sixth and eighth degrees of non-linearity is considered, the values of its energy spectrum are found.

Keywords: ordinary differential equation, anharmonic oscillator, wave function, generalized power series.

Bibliography link:

Belyaeva, I.N. The computer – assisted solution of the one – dimensional Schrödinger equation taking into account tunneling effects / I.N. Belyaeva, I.K. Kirichenko, O.D. Ptashnyi et al. // Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials: Interuniversity collection of proceedings / Ed. by V.M. Samsonov, N.Yu. Sdobnyakov. – Tver: TSU, 2019. – I. 11. – P. 283-290.

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