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Is it possible for a single proton to hold two electrons and still be stable? Yes, such a quantum system really exists: $H^-$ anions occur quite abundantly in alkali metal hydrides like $NaH$, $LiH$ and borohydride complex anions. They are stable but very powerful reducing agents, hence their frequent use in organic synthesis. Calculation of the bound ...

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I'll just explain the general idea that one has to keep in mind when setting up a perturbation expansion. One generally has to go through the following steps: Understand what you're expanding around. In quantum field theory, for example, one must be careful to expand around the vacuum of the theory (this is essentially what gives rise to the Higgs ...

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As mentioned in the comments by Bubble, this is answered in Ground State Energy Calculations for the Quartic Anharmonic Oscillator, Robert Smith. Notes for Math 4901, University of Minnesota, Morris (2013). but as the document is not crawlable by the Wayback Machine I'll summarize it here. Smith considers hamiltonians of the form  H=-\frac12 ...

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Most graduate text books in Classical mechanics have (as their last two chapters) discussions of perturbation theory in classical mechanics. These (however) are not invariably readable, and will usually restrict the solution to problems that can be described by a Hamiltonian e.g. have no friction or dissipation. Goldstein, "Classical Mechanics" has such a ...

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