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The normal definition of a potential energy is somewhat arbitrary.
Consider where a potential comes from: It appears when the total
energy (potential plus kinetic) is constant. But if something is
constant, we can add a number to it, and it is still constant!
Thus whether we define the gravitational potential at the surface
of the earth to be 0 or 100 J does not matter. Only differences
in potential energies play a rôle. It is customary to
define the potential ``far away'', as
| x|
to be zero.
That is a very workable definition, except in one case: if we take
a square well and make it deeper and deeper, the energy of the lowest
state decreases with the bottom of the well. As the well depth goes
to infinity, the energy of the lowest bound state reaches -
,
and so does the second, third etc. state. It makes much more
physical sense to define the bottom of the well to have zero energy,
and the potential outside to have value V0, which goes to infinity.
Next: 5.2 Solution
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