General solution of the Schrödinger Equation with Potential Field Quantization and Some Applications

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Hasan Hüseyin Erbil
Hasan Hüseyin Erbil
1 Ege University

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A simple procedure has been found for the general solution of the time-independent Schrödinger Equation (SE) with the help of quantization of potential area in one dimension without making any approximation.Energy values are not dependent on wave functions. So, to find the energy values, it is enough to find the classic turning points of the potential function. Two different solutions were obtained, namely, symmetric and anti symmetric in bound states. These normalized wave functions are always periodic. It is enough to take the integral of the square root of the potential energy function to find the normalized wave functions. If these calculations cannot be made analytically, they should then be performed by numerical methods. The SE has been solved for a particle in many one-dimension and the spherical symmetric central potential well, the relativistic theory of Dirac as examples.

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Hasan Hüseyin Erbil. 2019. \u201cGeneral solution of the Schrödinger Equation with Potential Field Quantization and Some Applications\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 19 (GJSFR Volume 19 Issue F1): .

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GJSFR Volume 19 Issue F1
Pg. 23- 86
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Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-F Classification: MSC 2010: 32W50
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v1.2

Issue date

April 19, 2019

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English

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A simple procedure has been found for the general solution of the time-independent Schrödinger Equation (SE) with the help of quantization of potential area in one dimension without making any approximation.Energy values are not dependent on wave functions. So, to find the energy values, it is enough to find the classic turning points of the potential function. Two different solutions were obtained, namely, symmetric and anti symmetric in bound states. These normalized wave functions are always periodic. It is enough to take the integral of the square root of the potential energy function to find the normalized wave functions. If these calculations cannot be made analytically, they should then be performed by numerical methods. The SE has been solved for a particle in many one-dimension and the spherical symmetric central potential well, the relativistic theory of Dirac as examples.

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General solution of the Schrödinger Equation with Potential Field Quantization and Some Applications

Hasan Hüseyin Erbil
Hasan Hüseyin Erbil Ege University

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