The Infinite Square Well
The infinite square well potential is given by:
This is illustrated below.
A particle under the influence of such a potential is free - no forces act - betweenand and is confined to that region by the need to have an infinite energy in order to travel outside that region. We can solve the equations describing the motion of the particle in each region and make them fit together at the boundaries using the conditions, for wavefunctionsand on either side of the barriers thatand
In the region of the well,and the Schrodinger equation becomes(1)
This has general solutionatandsince the potential is infinite there, sosoand
We can find the constantby requiring that the wavefunctionbe normalized soWe can differentiatetwice to getso from (1)