A particle is trapped in an infinite potential well. Describe what happens to the particle’s ground-state energy and wave function as the potential walls become finite and get lower and lower until they finally reach zero (U = 0 everywhere).
ground state energy of a particle in an infinite potential well is
when the potential well becomes finite with potential U the ground state energy is
where
is the penetration depth
The wave function extends to a distance of
outside the well and decays exponentially. The wave becomes
essentially 0 beyond
.
as U becomes less and less penetration of the wave beyond the
walls increases. The case where U=0
becomes imaginary , this the case where there are no potential
walls , the potential well is non-existing and particle is free .
This is the case the particle can be anywhere from -
to +
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