A bouncing particle
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(a) Construct quantities having the dimensions of energy and of length when the potential energy is V(z) = mgz for z > 0 and V(z) = 1 for z < 0.
(b) An electron bounces on a horizontal surface. In its lowest energy states, the electron stays near the surface, held there by gravity. Show that the minimum thickness of the layer in which the electron is likely to be found is about 1 mm. Why is this so large?
Note: Experiments have been done on very low-energy ("ultracold") bouncing neutrons.
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Solution Summary
The expert constructs quantities having the dimension of energy and of length for potential energy.
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Clearly, if we find a quantity with the dimensions of a length, L, we can multiply that by mg to obtain a quantity with the dimensions of energy, E:
E = m g L (1)
We can also use the equation E = h f = hbar omega to write down another expression for the energy by taking the ...
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