Solutions of the time-independent Schrödinger equation by uniformization on the unit circle

• Autorzy: Kazimierz Rajchel
• Języki publikacji: EN

Abstrakty

EN

The idea presented here of a general quantization rule for bound states is mainly based on the Riccati equation which is a result of the transformed, time-independent, one-dimensional Schrödinger equation. The condition imposed on the logarithmic derivative of the ground state function W0 allows to present the Riccati equation as the unit circle equation with winding number equal to one which, by appropriately chosen transformations, can be converted into the unit circle equation with multiple winding number. As a consequence, a completely new quantization condition, which gives exact results for any quantum number, is obtained.

Słowa kluczowe

EN

Schrödinger equation; Ricatti equation; unit circle; quantization condition

• Wydawca: Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
• Czasopismo: Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
• Rocznik: 2019
• Tom: 18
• Strony: 157-165

Daty

wydano

2019-09-25

Twórcy

autor

Kazimierz Rajchel

• Pedagogical University of Kraków, Institute of Computer Science

Bibliografia

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