hw4_PHYS3318 - is, n = 1. 4. Consider now a particle of...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
February 20, 2010 Cornell University, Department of Physics P3318, Analytical Mechanics, HW#4, due: 2/26/10, 2:30PM (at section) Question 1 : A symmetric well potential Consider a particle of mass m in the following one dimensional potential V ( x ) = ax 2 n , (1) where n is a positive integer and a > 0. 1. What are the units of a ? 2. Calculate the period of the particle as a function of its energy. You will need the following integral Z 1 - 1 dx ± 1 - x 2 n ² - 1 / 2 = 2 π Γ ³ 1 + 1 2 n ´ Γ ³ n + 1 2 n ´ - 1 . (2) 3. Show that the period is independent on the energy only for the harmonic case, that
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: is, n = 1. 4. Consider now a particle of mass m in a double well potential: V ( x ) = x 4 + bx 2 , ,b > , (3) First dene what are large and small energies and then nd what is approximately the period in these two cases? 5. Now consider the case where b < 0. What is approximately the period in the large and small energy cases? 1...
View Full Document

Ask a homework question - tutors are online