A particle in a box with the -function potential has been recently explored. We show that this example is solvable in the weak and the strong coupling limits. In either limit the attractive and repulsive potentials lead to identical spectra, with the possible exception of a single negative-energy state that is present when . We numerically obtain the spectra near the strong-coupling limit and discuss the consequences of the degeneracy that arises when .
REFERENCES
1.
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See, for example,
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In the strong-coupling limit the ground state for the attractive potential is at negative energy, and we do not consider it in the spectrum presented in Fig. 2.
6.
This expression is valid provided .
7.
This contribution also vanishes in the weak-coupling limit, , and is consistent with the results in Ref. 4.
© 2009 American Association of Physics Teachers.
2009
American Association of Physics Teachers
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