Ramp in Square Well
المؤلف:
Sidney B. Cahn, Gerald D. Mahan And Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 2 , p 66
19-8-2016
1713
Ramp in Square Well
A particle of mass m is bound in a square well where –a/2 < x < a/2.
a) What are the energy and eigenfunction of the ground state?
b) A small perturbation is added, V(x) = 2ε|x|/a. Use perturbation theory to calculate the change in the ground state energy to O(ε).
SOLUTION
a) For a particle bound in a square well that runs from –a/2 < x < a/2, the eigenfunction and eigenvalue for the lowest energy state are
(1)
(2)
The eigenfunction is symmetric and vanishes at the walls of the well.
b) We use first-order perturbation theory to calculate the change in energy from the perturbation:
(3)
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