Süperintegrallenebilir kuantum osilatör ve coulomb sistemleri
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Date
2015
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Publisher
Trakya Üniversitesi Fen Bilimleri Enstitüsü
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info:eu-repo/semantics/openAccess
Abstract
Bu çalışmada matematiksel fizikte çok iyi bilinen kepler, hidrojen atomu ve harmonik osilatör sistemleri ele alınmaktadır. Maksimal süperintegrallenebilir olan bu sistemler beş bağımsız hareket integrallerine sahiptir. Klasik sistemler için bu hareket integralleri (Newton denklemini çözmeden) yörüngelerin bulunmasında; kuantum sistemler için ise (Schrödinger denklemini çözmeden) enerji spektrumunun bulunmasında kullanılmıştır.
abstract
In this master thesis we deal with the most well-known Hamiltonian systems in mathematical physics : the Kepler system , the hydrogen atom and the harmonic oscillator. These systems are maximally superintegrable and possess five independent integrals of motion for classical systems these integrals of motion are used to obtain the trajectories without solving Newton equation while for quantum ones they are used to obtain the energy spectrum without solving the Schrödinger equation.
abstract
In this master thesis we deal with the most well-known Hamiltonian systems in mathematical physics : the Kepler system , the hydrogen atom and the harmonic oscillator. These systems are maximally superintegrable and possess five independent integrals of motion for classical systems these integrals of motion are used to obtain the trajectories without solving Newton equation while for quantum ones they are used to obtain the energy spectrum without solving the Schrödinger equation.
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Keywords
Coulomb Kuantum Sistemleri, Maksimal Süperintegrallenebilir, Kuantum Osilatör, Coulomb Quantum Systems, Maximal Superintegrability, Quantum Oscillator
