Second-Order Field Strength Energy Spectrum of Spherical Shell

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eman2009
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what the energy spectrum to second order in the field strength for a spherical shell?
 

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Forgive my inorance, but I am not familiar with a quantum system that is referred to as 'a spherical shell', my best guess would be 'spherical well' but that would still not unambiguously determine the field strength. Perhaps it's just me, but maybe you could provide a clarification, what is the Hamiltonian for this system?
 

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