Quantum Mechanics Solution Manual 

© Leon van Dommelen 

3.5.8.1 Solution pipega
Question:
If the cross section dimensions and are one tenth the size of the pipe length, how much bigger are the energies and compared to ? So, by what percentage is the onedimensional ground state energy as an approximation to the threedimensional one, , then in error?
Answer:
The energies are
If and are ten times smaller than then and are each 100 times larger than . So the onedimensional ground state energy is smaller than the true ground state energy by a factor 201. Which means it is off by 20 000%.