Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials
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Accounting of tunneling effects when calculating the energy spectrum of the Schrödinger equation

I.N. Belyaeva1, N.A. Chekanov1, I.K. Kirichenko2, N.N. Chekanova3

1Belgorod National Research University, Belgorod, Russia

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

3Kharkiv Educational and Research Institute of the Higher Educational Institution «University of Banking», Kharkiv, Ukraine

DOI: 10.26456/pcascnn/2019.11.291

Abstract: The general scheme of the method for integrating second-order differential equations in the form of power series is presented. The obtained results for the Schrödinger equation with potentials with two and three minima for quantum anharmonic oscillators are presented. The necessary accuracy of calculations is controlled by the number of terms in the power series and the number of digits in the mantissa of decimal numbers. The structure of the energy levels and wave functions are shown.

Keywords: ordinary differential equation, energy spectrum, wave function, generalized power series.

Bibliography link:

Belyaeva, I.N. Accounting of tunneling effects when calculating the energy spectrum of the Schrödinger equation / I.N. Belyaeva, N.A. Chekanov, I.K. Kirichenko 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. 291-297.

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