Particle in an Infinite Vee Potential

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This Demonstration considers solutions of the Schrödinger equation for a particle in a one-dimensional "infinite vee" potential: , setting
for simplicity. The solutions of the differential equation that approach zero as
are Airy functions
, as can be found using DSolve in Mathematica. The allowed values of
are found by requiring continuity of
at
. The even solutions
require
, which leads to
, with
,
,
, … being the first, second, third, … zeros of the Airy prime function:
. The odd solutions
have nodes
, which leads to
, with
,
,
, … being the first, second, third, … zeros of the Airy function:
. The ground state is given by
.
Contributed by: S. M. Blinder (November 2010)
Open content licensed under CC BY-NC-SA
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