نموذج نظري للجمل الكمومية بسويتي طاقة
Abstract
قدمنا في هذا العمل نموذجاً نظرياً لدراسة اهتزازات جملة كمومية بسويتي طاقة مفترضين وجود تفاعل متبادل بينهما من خلال:
أولاً: تمثيل الجملة الكمومية ذات سويتي الطاقة بحفرتي كمون كموميتين لانهائيتين متآثرتين على بعد واحد x ومتناظرتين بالنسبة لمبدأ الإحداثيات o، ثمّ إيجاد المتجهات الخاصة والقيم الخاصة لهما باستخدام معادلة شرودنغر المستقرّة Stationary Schrödinger’s equation.
ثانياً: إثبات أنّ التقريب غير الاضطرابي كاف لكتابة مؤثر الهاملتوني لهذه الجملة، ولاشتقاق معادلة رابي للجملة Rabi’s equation، وتطبيقها مباشرة على مؤثر التطور للحالة الابتدائية للجملة.
We present a theoretical model for studying the oscillations among two-level quantum system when an interaction term is considered:
First, we present the two-level quantum system with a symmetric double square potential well in interaction, in one dimension x, then we find the eigenvectors and the eigenvalues for this system by solving the stationary Schrödinger’s equation.
Second, we proved that a nonperturbative approach can be conveniently used to write the Hamiltonian operator and to derive the Rabi’s equation for this system, directly applying the time evolution operator to the initial state of the system.
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