Abstract
This research paper presents a new method: the integral Rohit
transform to study and solve quantum physics problems. The standard
calculus approach is typically used to solve quantum mechanics issues.
The obtained solutions demonstrate the potential and efficacy of the
suggested approach to overcoming quantum mechanical problems,
such as low-energy particle scattering by a completely rigid sphere
and particle behavior in a one-dimensional infinitely high potential
box. The successful application of the integral Rohit Transform has
been demonstrated in solving the one-dimensional time-independent
Schrodinger’s equation. This application has yielded results that include
the determination of eigenenergy values and eigenfunctions for a
particle confined within an infinitely high potential well, as well as the
calculation of the total scattering cross-section for low-energy particles
interacting with a perfectly rigid sphere. In the case of low energy
limit, the total scattering cross-section for low energy particles due to a
perfectly rigid sphere, as determined through quantum mechanics, is
equivalent to the geometrical cross-section of said sphere. Additionally,
the energy values that the particle can possess within a one-dimensional
infinitely high potential well demonstrate that the energy of said particle,
when confined within this potential well, is quantized.
transform to study and solve quantum physics problems. The standard
calculus approach is typically used to solve quantum mechanics issues.
The obtained solutions demonstrate the potential and efficacy of the
suggested approach to overcoming quantum mechanical problems,
such as low-energy particle scattering by a completely rigid sphere
and particle behavior in a one-dimensional infinitely high potential
box. The successful application of the integral Rohit Transform has
been demonstrated in solving the one-dimensional time-independent
Schrodinger’s equation. This application has yielded results that include
the determination of eigenenergy values and eigenfunctions for a
particle confined within an infinitely high potential well, as well as the
calculation of the total scattering cross-section for low-energy particles
interacting with a perfectly rigid sphere. In the case of low energy
limit, the total scattering cross-section for low energy particles due to a
perfectly rigid sphere, as determined through quantum mechanics, is
equivalent to the geometrical cross-section of said sphere. Additionally,
the energy values that the particle can possess within a one-dimensional
infinitely high potential well demonstrate that the energy of said particle,
when confined within this potential well, is quantized.
Keywords
Quantum Mechanics Problems; Integral Rohit Transform; Perfectly Rigid Sphere Infinite Potential Well.
Abstract
يقدم هذا البحث طريقة جديدة وهي تحويل روهيت التكاملي لدراسة مسائل فيزياء الكم وايجاد الحلول الدقيقة لها. عادة ما يتم استخدام نهج حساب التفاضل والتكامل لحل مشكلات ميكانيكا الكم. نتائج هذا البحث تبين امكانات وفعالية النهج المقترح للتغلب على مشكلات ميكانيكا الكم مثل تشتت الجسيمات منخفضة الطاقة بواسطة كرة صلبة وسلوك الجسيمات في صندوق احادي البعد عالي الجهد باستخدام تحويل روهيت التكاملي. وقد اسفر هذا التطبيق عن نتائج تتضمن تحديد قيم الطاقة الذاتية ودوالها الذاتية لجسيم محصور داخل بئر جهد عالي بلا حدود، فضلا عن حساب المقطع العرضي للتشتت الكلي للجسيمات منخفضة الطاقة بسبب كرة صلبة، كما تم تحديده من خلال ميكانيكا الكم، يعادل المقطع العرضي الهندسي للكرة المذكورة. بالاضافة الى ذلك، فان قيم الطاقة التي يمكن ان يمتلكها الجسيم داخل بئر جهد عالي بلا حدود احادي البعد تثبت ان طاقة الجسيم المذكور يمكن حسابها عندما يكون محصورا داخل بئر الجهد.
Keywords
بئر الجهد اللانهائي
تحويل روهيت المتكامل
كرة صلبة كليا
مشاكل ميكانيكا الكم