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Unformatted text preview: uncertainty in energy. If you could bring a macroscopic particle truly into a single
energy eigenstate, it too would have no position. And the smallest thing you might do to
ﬁgure out where it is would kick it out of that single energy state. 3.5.8 Threedimensional solution 3.5.8.1 Solution pipega Question: If the cross section dimensions ℓy and ℓz are one tenth the size of the pipe length,
how much bigger are the energies Ey1 and Ez1 compared to Ex1 ? So, by what percentage is
the onedimensional ground state energy Ex1 as an approximation to the threedimensional
one, E111 , then in error?
Answer: The energies are
Ex1 h2 π 2
¯
=
2mℓ2
x Ey1 h2 π 2
¯
=
2mℓ2
y Ez1 h2 π 2
¯
=
.
2mℓ2
z If ℓy and ℓz are ten times smaller than ℓx th...
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This note was uploaded on 11/13/2011 for the course PHY 4458 taught by Professor Garvin during the Fall '11 term at University of Florida.
 Fall '11
 GARVIN

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