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Please use this identifier to cite or link to this item: http://hdl.handle.net/11129/3791

Title: The Exact Solutions in Quantum Mechanics
Authors: Mazharimousavi, Habib
Rammoo, Mohammed Noor Sedeeq
Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Physics
Keywords: Physics
Quantum theory - Nuclear physics - Quantum field theory
One-dimensional infinite well
Time-dependent potential
Exact solution
Coherent state
Issue Date: Aug-2014
Publisher: Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)
Citation: Rammoo, Mohammed Noor Sedeeq. (2014). The Exact Solutions in Quantum Mechanics. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Physics, Famagusta: North Cyprus.
Abstract: In this study we consider two different and particular quantum systems. The first system is a one-dimensional particle confined within an infinite well with the left wall at rest and the right wall moving with or without acceleration. This is a quantum configuration with time-dependent Hamiltonian where the conservation of energy does not hold anymore. Our task in this problem is to solve the correspondence time dependent Schrödinger equation and find the energy eigenvalues and eigenfunctions. The second system is a particle which undergoes a modified radial attraction force in two dimensions. The modification is such that the corresponding potential depends on not only the radial coordinate but also the polar angle. We find the energy spectrum of the particle and using the concept of coherent states, we show that the classical trajectory of a classical particle directed by a similar radial potential is almost the same as the predicted probability density of the quantum particle by the coherent states. Keywords: One-dimensional infinite well, Time-dependent potential, Exact solution, Coherent state.
ÖZ : Bu tezde iki farklı özel kuantum sistemi incelenmektedir. Birinci sistemde sol duvarı sabit , sağ duvarı ivmeli /ivmesiz hareketli bir kutu içerisindeki tek boyutlu partikül ele alınıyor. Zamana bağımlı Hamilton fonksiyonu nedeniyle enerji korunumu sağlanmıyor.Zamana bağımlı Schrödinger denklemini kullanarak enerji uygun değer ve fonksiyonları bulunuyor. İkinci sistem ise iki boyutlu modife edilmiş çekim kuvveti için partikül incelenmektedir. Burada potansiyel hem radial hemde açısal bağımlılık içermektedir. Düzgün durumlar kullanarak partikül enerji spektrumu bulunmuştur.Klasik partikül yörüngesi ile düzgün durum kuantum olasılık dağılımı arasındaki sıkı benzerlik ortaya konmaktadır. Anahtar.kelimeler.:.Bir boyutlu sonsuz kuyu, zamana bağlı potansiyel , düzgün durum fonksiyonu
Description: Master of Science in Physics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Physics, 2014. Supervisor: Assoc. Prof. Dr. Habib Mazharimousavi.
URI: http://hdl.handle.net/11129/3791
Appears in Collections:Theses (Master's and Ph.D) – Physics

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