Energies for a Heaviside-Lambda Potential Well

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This Demonstration calculates the bound energy levels of a particle in an inverted Heaviside-lambda (vee-shaped) potential well of depth and width
, using the semiclassical Wentzel–Kramers–Brillouin (WKB) method. The numerical results are within 1% of the values that would be obtained from the exact solutions of the corresponding Schrödinger equation. The energies are determined by the Sommerfeld–Wilson quantization conditions
. With
, the integral reduces to
, noting that
are the classical turning points. This can be solved for the energy levels:
,
. The highest bound state is given by
, where
is the floor, which for positive numbers is simply the integer part.
Contributed by: S. M. Blinder (March 2011)
Open content licensed under CC BY-NC-SA
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Details
For a discussion of the WKB method, see the Demonstration "WKB Computations on Morse Potential".
Permanent Citation
"Energies for a Heaviside-Lambda Potential Well"
http://demonstrations.wolfram.com/EnergiesForAHeavisideLambdaPotentialWell/
Wolfram Demonstrations Project
Published: March 7 2011