Energies for a Heaviside-Lambda Potential Well

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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



For a discussion of the WKB method, see the Demonstration "WKB Computations on Morse Potential".

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.