Question

Consider a hydrogen atom where the electron is replaced by a spinless ideal point-like particle (i.e., you can neglect corrections arising from the Darwin term) of the same mass and electric charge, and the proton is replaced by another positively charged particle which is 105 times heavier. The structure corrections are in general O ~ mec^2/a^4. (a) Which kind of perturbation theory is needed to study this system and why? (b) When would you expect a first-order correction in the energy arising out of this external electric field? Explain with proper logic and necessary calculations. (c) Is it possible to get a direct second-order (i.e., no first-order) correction in the energy for the same perturbation? Explain with proper logic and necessary calculations.

          Consider a hydrogen atom where the electron is replaced by a spinless ideal point-like particle (i.e., you can neglect corrections arising from the Darwin term) of the same mass and electric charge, and the proton is replaced by another positively charged particle which is 105 times heavier. The structure corrections are in general O ~ mec^2/a^4.

(a) Which kind of perturbation theory is needed to study this system and why?

(b) When would you expect a first-order correction in the energy arising out of this external electric field? Explain with proper logic and necessary calculations.

(c) Is it possible to get a direct second-order (i.e., no first-order) correction in the energy for the same perturbation? Explain with proper logic and necessary calculations.

3 consider a hydrogen atom where the electron is replaced by a spinless ideal point like particle ie you can neglect correction arising from darwin term of the same mass and electric charge 69433

Added by Frank K.

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