Linear Potential I
المؤلف:
Sidney B. Cahn, Gerald D. Mahan And Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 2 , p 63
18-8-2016
1716
Linear Potential I
A particle of mass m is bound in one dimension by the potential V(x) = |Fx|, where F is a constant. Use variational methods to estimate the energy of the ground state.
SOLUTION
The potential V(x) is symmetric. The ground state eigenfunction must also be symmetric and have no cusps. A simple choice is a Gaussian:
(1)
where the variational parameter is α and A is a normalization constant. Again we must evaluate the three integrals in (A.3.1)–(A.3.4):
(2)
(3)
(4)
(5)
The minimum energy is found at the value α0, where the energy derivative with respect to α is a minimum:
(6)
(7)
(8)
الاكثر قراءة في مواضيع اخرى
اخر الاخبار
اخبار العتبة العباسية المقدسة
