ضرایب سوق مستقل از زمان برای پتانسیل‌های شکل‌ناوردا

نوع مقاله : مقاله پژوهشی کامل

نویسندگان

گروه فیزیک، دانشکده علوم، دانشگاه گلستان، گرگان، ایران

چکیده

در این تحقیق، با استفاده از حل تحلیلی معادله‌ی فوکر-پلانک، ضرایب سوق مستقل از زمان برای پتانسیل‌های شکل‌ناوردا به‌دست آمده‌اند. در این رهیافت، ابتدا معادله‌ی فوکر-پلانک به یک معادله‌ی شرودینگرگونه تبدیل می‌شود. سپس، با استفاده از سازوکار مکانیک کوانتومی ابرتقارنی، معادله‌ی فوکر-پلانک به‌طور تحلیلی حل شده و جواب‌های صریح آن به‌دست می‌آیند. در این محاسبه، ضریب پخش، به‌صورت یک ثابت در نظر گرفته شده است. این رهیافت برای پتانسیل‌های شکل‌ناوردا که پتانسیل‌های دقیقاً قابل حل هستند، کاربرد دارد. پتانسیل‌های دقیقاً قابل حل، به پتانسیل‌هایی اطلاق می‌شود که همه‌ی ویژه‌مقادیر و ویژه‌توابع مربوطه را می‌توان برای آنها صریحاً به‌دست آورد. بررسی توزیع چگالی احتمال باریکه‌ی کربنی شتاب‌گرفته از لیزر را در روش اشتعال سریع، بعد از ورود به ناحیه‌ی سوخت، به‌عنوان یک کاربرد از این محاسبات ارائه شده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Time Independent of Drift Coefficients for Shape Invariant Potentials

نویسندگان [English]

  • Taha Koohrokhi
  • Abdolmajid Izadpanah
  • Atefeh Shadmehr
Department of Physics, Faculty of Sciences, Golestan University, Gorgan, Iran
چکیده [English]

In this research, using the analytical solution of the Fokker-Planck equation, the time-independent drift coefficients for the shape-invariant potentials have been obtained. In this approach, first, the Fokker-Planck equation is converted into a Schrödinger-like equation. Then, using the mechanism of supersymmetric quantum mechanics, the Fokker-Planck equation is analytically solved and its explicit solutions are obtained. In this calculation, the diffusion coefficient is considered a constant. This approach is applicable to shape-invariant potentials which are exactly solvable potentials. Exactly solvable potentials refer to potentials for which all eigenvalues and eigenfunctions can be obtained explicitly. These calculations are used to examine the probability density distribution of laser-accelerated carbon beams after entering the fuel region in the fast ignition method.

کلیدواژه‌ها [English]

  • Fokker-Plank Equation
  • Drift Coefficient
  • Diffusion Coefficient
  • Supersymmetric Quantum Mechanics
  • Superpotential
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