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Unformatted text preview: >a V HxL = Our energy eigenstates satisfy the time-independent Schrödinger equation inside and outside the barrier
— 2 B- 2 m
„ 2 „ x2 „2
„ yHxL = E yHxL 2 „ x2 HoutsideL + V0 F yHxL = E yHxL HinsideL yHxL = - 2mE yHxL = - 2 m HE - V0 L —2 yHxL —2 HoutsideL
yHxL HinsideL Solutions to the equation outside of the barrier arePrinted by Mathematica for Students the region to the left of the barrier (x < 0), the
complex exponentials. In
solution is a superposition of an incoming incident wave (‰Â k x ) and an outgoing reflected wave (‰-Â k x ). Solutions to the equation
inside of the barrier (0 § x § a) for E < V0 are real exponentials and will in general be a superposition of a decay term (‰-q x )
and a growing term (‰q x ). Neither of these terms is zero a priori because there will be a reflected and transmitted contribution Our energy eigenstates satisfy the time-independent Schrödinger equation inside and outside the barrier
—2 8 -2m „2 yHxL = E yHxL „ x2
—2 „ 2
B- 2 m 2 + V0 F yHxL
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This note was uploaded on 02/01/2014 for the course PHYC 491/496 taught by Professor Akimasamiyake during the Fall '13 term at New Mexico.
- Fall '13