Quantum Mechanics Solution Manual 

© Leon van Dommelen 

3.5.8.2 Solution pipegb
Question:
At what ratio of does the energy become higher than the energy ?
Answer:
Using the given expression for ,
when
Canceling the terms that both sides have in common:
and canceling the common factors and rearranging:
So when 0.61 or more, the third lowest energy state is given by rather than . Obviously, it will look more like a box than a pipe then, with the dimension 61% of the dimension.