Quantum Engi Q and A_Part_9

# If you could bring a macroscopic particle truly into

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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 Three-dimensional solution 3.5.8.1 Solution pipeg-a 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 one-dimensional ground state energy Ex1 as an approximation to the three-dimensional 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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