Yıl 2018, Cilt 42 , Sayı 5, Sayfalar 527 - 572 2018-10-12

General solution of the Schrödinger equation with potential field quantization

Hasan Hüseyin ERBİL [1]


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 antisymmetric 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 wells as examples. Their energies and normalized wave functions were found as examples. These solutions were also applied to the theories of scattering and alpha decay. The results obtained with the experimental values were compared with the calculated values. One was seen to be very fit.

Potential quantization, Schrödinger equation, infinitely high potential well, potential wells of any form, -decay theory, scattering, energy values of states
  • Büyükkılıç, F.; Eğrifes, H.; Demirhan, D. Theor. Chem. Acc. 1997 , 98 , 192-196.
  • Eğrifes, H.; Demirhan, D.; Büyükkılıç, F. Phys. Scripta 1999 , 59 , 90-94.
  • Eğrifes, H. ; Demirhan, D.; Büyükkılıç, F. Phys. Scripta 1999 , 60 , 195-198.
  • Eğrifes, H. ; Demirhan, D.; Büyükkılıç, F. Phys. Lett. A 2000 , 275 , 229-237.
  • Powell, J. L.; Crasemann, B. Quantum Mechanics ; Addison-Wesley Publising Company Inc.: USA, 1965.
  • Schwabl, F. Quantum Mechanics , 2nd ed.; Springer-Verlag Berlin Heidelberg: New York, NY, USA, 1995.
  • Griffiths, D. J. Introduction to Quantum Mechanics ; Pearson Prentice Hall: NJ, USA, 1995.
  • Erbil, H. H. The International Review of Physics Vol. 1 2007 , 4 , 197-213.
  • Greiner, W. Quantum Mechanics , 2nd ed.; Springer-Verlag Berlin Heidelberg: New York, NY, USA ; 1993.
  • Cooper, F.; Khare, A.; Sukhatme, U. Supersymmetry in Quantum Mechanics ; World Scientific, 2001.
  • Gönül, B.; Zorba, İ. Phys. Lett. A 2000 , 269 , 83-88.
  • Gonul, B.; Ozer, O.; Koçak, M.; Tutcu, D.; Cançelik, Y. J. Phys. A: Math. Gen. 2001 , 34 , 8271-8279.
  • Griffiths, J. Introduction to Quantum Mechanics ; Prentice Hall, 1994.
  • Kasap, E.; Gönül, B.; Şimşek, M. Chem. Phys. Lett. 1990 , 172, 499-502.
  • Landau, L. D.; Lifstits, E. M. Quantum Mechanics ; Pergamon Press, 1958.
  • Hassani, S. Foundations of Mathematical Physics ; Prentice-Hall International Inc.: USA, 1991.
  • Ayant, Y.; Borg, M. Fonctions Speciales ; Dunod: Paris, France, 1971.
  • Messiah, A. Quantum Mechanics ; North Holland, 1958.
  • Erbil, H. H. The International Review of Physics Vol. 2 2008 , 1 , 1-10.
  • Pal, M. K. The Theory of Nuclear Structure ; Scientific and Academic Editions, 1983.
  • Erbil, H. H,; Ertik. H.; Şirin, H.; Kunduracı, T. The International Review of Physics 2012 , 6 , 359-366.
  • Volya, A. http//www.volya.net.
  • Erbil, H. H. The International Review of Physics 2013 , 7, 376-384.
  • Krane, K. S. Introductory Nuclear Physics ; John-Wiley & Sons: New York, NY, USA, 1988.
  • Firestone, R. B. Table of Isotopes ; Wiley Interscience, 1996.
  • Harmatz, B. Nucl. Data Sheets 1981 , 34, 1-807.
  • Schmorak, M. R. Nucl. Data Sheets 1990 , 45 , 1-207.
  • Rytz, A. At. Data Nucl. Data Tables 1991 , 47 , 205-239.
  • Rytz, A. At. Data Nucl. Data Tables 1979 , 23 , 507-598.
  • Rytz, A. At. Data Nucl. Data Tables 1973 , 12 , 407-498.
  • Schmorak, M. R. Nucl. Data Sheets, 1981 , 32 , 1-209.
  • Avrigeanu, M.; Von Oertzen W.; Fischer, U.; Avrigeanu, V. Nucl. Phys. A 2005 , 759, 327-341.
  • Erbil, H. H.; Selvi, A. S.; Kunduracı, T. The International Review of Physics 2013 , 7, 230-238.
  • Erbil, H. H. The International Review of Physics 2012 , 6 , 144-152.
  • Erbil, H. H. The International Review of Physics 2012 , 6, 439-447.
  • Erbil, H. H,; Kunduracı, T. The International Review of Physics, 2012 , 6 , 269-278.
  • Erbil, H. H. Kuantum Fiziği ; Ege University: İzmir, Turkey, 2001.
  • Mughabghab, S. F.; Divadeenam, M.; Holden, N. E. Neutron Cross Sections ; Academic Press Inc.: New York, NY, USA, 1981.
  • Mughabghab, S. F. Thermal Neutron Capture Cross Section, Resonance Integrals and G-Factors , International Nuclear Data Committee, Vienna, 2003.
  • Mughabghab, S. F.; Divadeenam, M.; Holden, N. E. Neutron Cross Sections 1/A; Academic Press Inc.: London, UK, 1981
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Orcid: 0000-0001-7694-8541
Yazar: Hasan Hüseyin ERBİL

Tarihler

Yayımlanma Tarihi : 12 Ekim 2018

Bibtex @araştırma makalesi { tbtkphysics488458, journal = {Turkish Journal of Physics}, issn = {1300-0101}, eissn = {1303-6122}, address = {}, publisher = {TÜBİTAK}, year = {2018}, volume = {42}, pages = {527 - 572}, doi = {}, title = {General solution of the Schrödinger equation with potential field quantization}, key = {cite}, author = {Erbil, Hasan Hüseyin} }
APA Erbil, H . (2018). General solution of the Schrödinger equation with potential field quantization . Turkish Journal of Physics , 42 (5) , 527-572 . Retrieved from https://dergipark.org.tr/tr/pub/tbtkphysics/issue/40616/488458
MLA Erbil, H . "General solution of the Schrödinger equation with potential field quantization" . Turkish Journal of Physics 42 (2018 ): 527-572 <https://dergipark.org.tr/tr/pub/tbtkphysics/issue/40616/488458>
Chicago Erbil, H . "General solution of the Schrödinger equation with potential field quantization". Turkish Journal of Physics 42 (2018 ): 527-572
RIS TY - JOUR T1 - General solution of the Schrödinger equation with potential field quantization AU - Hasan Hüseyin Erbil Y1 - 2018 PY - 2018 N1 - DO - T2 - Turkish Journal of Physics JF - Journal JO - JOR SP - 527 EP - 572 VL - 42 IS - 5 SN - 1300-0101-1303-6122 M3 - UR - Y2 - 2018 ER -
EndNote %0 Turkish Journal of Physics General solution of the Schrödinger equation with potential field quantization %A Hasan Hüseyin Erbil %T General solution of the Schrödinger equation with potential field quantization %D 2018 %J Turkish Journal of Physics %P 1300-0101-1303-6122 %V 42 %N 5 %R %U
ISNAD Erbil, Hasan Hüseyin . "General solution of the Schrödinger equation with potential field quantization". Turkish Journal of Physics 42 / 5 (Ekim 2018): 527-572 .
AMA Erbil H . General solution of the Schrödinger equation with potential field quantization. Turkish Journal of Physics. 2018; 42(5): 527-572.
Vancouver Erbil H . General solution of the Schrödinger equation with potential field quantization. Turkish Journal of Physics. 2018; 42(5): 527-572.
IEEE H. Erbil , "General solution of the Schrödinger equation with potential field quantization", Turkish Journal of Physics, c. 42, sayı. 5, ss. 527-572, Eki. 2018