01 تیر 1403
خسرو سايوند

خسرو سایوند

مرتبه علمی: استاد
نشانی: ملایر گروه ریاضی دانشگاه ملایر
تحصیلات: دکترای تخصصی / ریاضی
تلفن: 081-33398981
دانشکده: دانشکده علوم ریاضی و آمار

مشخصات پژوهش

عنوان
Reanalysis of an open problem associated with the fractional Schr¨odinger equation
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها
fractional Schrodinger equation, infinite potential well, Riesz fractional derivative, Mittag– Leffler function
سال
2016
مجله THEORETICAL AND MATHEMATICAL PHYSICS
پژوهشگران خسرو سایوند

چکیده

It was recently shown that there are some difficulties in the solution method proposed by Laskin for obtaining the eigenvalues and eigenfunctions of the one-dimensional time-independent fractional Schr¨odinger equation with an infinite potential well encountered in quantum mechanics. In fact, this problem is still open. We propose a new fractional approach that allows overcoming the limitations of some previously introduced strategies. In deriving the solution, we use a method based on the eigenfunction of the Weyl fractional derivative. We obtain a solution suitable for computations in a closed form in terms of the Mittag–Leffler functions and fractional trigonometric functions. It is a simple extension of the results previously obtained by Laskin et al.