# Finite potential well

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Finite potential well

The finite potential well (also known as the finite square well) is a simple problem from quantum mechanics. It is an extension of the infinite potential well, in which a particle is confined to a box, but one which has finite - not infinite - potential walls. This means unlike the infinite potential well, there is a probability associated with the particle being found outside of the box. The quantum mechanical interpretation is unlike the classical interpretation, where if the total energy of the particle is less than potential energy barrier of the walls it cannot be found outside the box. In the quantum interpretation, there is a non-zero probability of the particle being outside the box even when the energy of the particle is less than the potential energy barrier of the walls (because of quantum tunnelling).

The particle in a 1-dimensional box

For the 1-dimensional case on the "x"-axis, the time-independent Schrödinger equation can be written as:

::

ee also

*Potential well
*Delta function potential
*Infinite potential well
*Semicircle potential well
*Quantum tunnelling

References

*cite book | author=Griffiths, David J. | title=Introduction to Quantum Mechanics | edition = 2nd ed. | publisher=Prentice Hall | year=2005 | id=ISBN 0-13-111892-7

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