When the classical & quantum mechanical considerations hint to a single point; a microscopic particle in a one dimensional box with two infinite walls and a linear potential inside it
الموضوعات : Journal of Physical & Theoretical ChemistryM. Monajjemi 1 , K. Zare 2 , A.R. Zieglari 3
1 - Department of Chemistry, Islamic Azad University, Science and Research
Campus, Poonack, P.O. Box :14515 - 775, Tehran, Iran
2 - Not-mentioned
3 - Not-mentioned
الکلمات المفتاحية: One-dimensional Schrödinger eq, Bessel generalized differentia, Bessel functions,
ملخص المقالة :
In this paper we have solved analytically the Schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. Based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square of the linear momentum are equal to the classical time average of particle position and its square of the linear momentum, respectively.
