في هذه الرسالة نقدم مفاهيم أساسية ذات علاقة بفضاءات الضرب الداخلي وتضاءات هلبرت، ثم نقدم معادلة شرودنجر والتي تكتسب أهميتها في مجالات عدة وأهمها الفيزياء. ً ندرس المعادلة المعتمدة على الزمن وكذلك المستقلة عن الزمن ونضرب مثالا على حلها لحالة المتذبذب التواتقي البسيط والذي سيكون نواة لموضوع هذه الرسالة وهو الحل العددي لمعادلة شرودنجر. نناقش بعدئذ الحل العددي لمعادلة شرودنجر بطريقة مبتكرة والتي تسمى بطريقة الجهد المتشكلة وإتتمام الحسابات في الحالة الأرضية لمنظومة الإسناد وهي منظومة المتذبذب التوافقي البسيط، نقدم النتائج التي توصلنا إليها باستخدام الطرق العددية المعروفة وهي طريقة الفروق المنتهية وطريقة رنج-كوتا. ختام ً نعطي مناقشة مقتضبة حول أعمال مستقبلية يمكن القيام بها وتتضمن إجراء حسابات مماثلة للحالات المثارة للمتذبذب التوافقي البسيط وكذلك إجراء الحسابات باستخدام نظرية التشويش من الرتبة الأولى والمقارنة بين الحسابات الناتجة من طريقة الجهد المتشكلة وطريقة التشويش.
خديجة عبد العاطي بن موسي (2014)

: Neodymium isotopes (Z=60) lie in the traditional rotational to transitional-spherical region that occurs at the range of deformed nuclei. The identity of 146−158 Neodymium nuclei have been determined in framework of Interacting Boson Model-2, a simulation program with NPBOS has been used to obtain the theoretical energy levels for Neodymium isotopes. The parameters of the best fit to the measured data are determined. The energy positive parity bands of those isotopes were calculated using (IBM-2) and then it compared with the experimental values. The mentioned isotopes ratios (E(4_1^+))/(E(2_1^+)) have calculated and also E-GOS curves (( E_γ)/I) have drawn as a function of the spin I, to classify symmetry of the nuclei. The electromagnetic transition probabilities B(E2) of these nuclei was calculated as well, where a good agreement for low lying energy states were obtained between experimental results and theoretical calculations. The results have been shown that the interested nuclei 152-158Nd have rotational characters SU (3), and O (6) symmetry is substantiated for 146-148Nd, as well as the critical point X (5) has been determined for 150Nd isotope.
D. Nasef, Najat S. Eshaftri, Ayad E. Ezwam, Suad M. Bogrin, Asma A. Elbendag, Sadiq M. El-kadi(12-2021)

Abstract In this work, study was performed using Amorphous polymer – based composites consisting of polystyrene (PS) and carbon black (CB) . Five samples have been prepared with different weight percentage which are (0%CB+100%PS) , (5%CB+95%PS) , (15%CB+85%PS) , (25%CB+75%PS) and (35%CB+65%PS) . The electrical properties have been studied for these samples as follows : Electrical conductivity , relative dielectric constant and the dielectric loss tangent were measured at alternating electric field in temperature range between (30C°) and (60C°) and at four different constant frequencies (100HZ, 1KHZ, 10KHZ and 100KHZ ) . It is noted that the highest value of alternating electrical conductivity at (30C°) is for the sample of composition (25%CB+75%PS) which was (1.25x10 S/m ) and the highest value at temperature (60C°) was for same sample with value of (3.2x10 S/m ) , it should be noted that in general the electrical conductivity increases as the temperature increases where this result shows the behaviour of semiconductors. The relative dielectric constant in the pure sample (0%CB+100%PS) and the other samples with low percentage of carbon black increases as the temperature increases however it decreases as frequency increases. And the samples with higher percentage of carbon black which are (25%CB+75%PS) and (35%CB+65%PS) it was noted that the relative dielectric constant decreases as temperature increases. The lowest value was (1.26) at temperature (30C°) and frequency (10KHZ) for the sample with composition of (15%CB+85%PS), while the highest value at same temperature is (410.2) at (100HZ) for the sample with composition of (25%CB+75%PS), for the relative dielectric constant the highest result it was for the sample (5%CB+95%PS) at (607) at (100HZ) and (45C°). The dielectric loss tangent increases as the carbon black increases in all samples and it was found that the temperature influence will be at high percentage of the carbon black where the temperature of (55C°) the dielectric loss tangent increased to the highest value (1.2X10 ) for the sample of composition (35%CB+65%PS). at the high level of the carbon black it was found that the dielectric loss tangent decreases as the frequency increases.
عادل محمد التميمي (2013)