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## Main Question or Discussion Point

In theory, does an algebraic expression exist for the ground state of the Klein Gordon equation with [itex]\phi^4[/itex] interactions in the same way an algebraic expression exists for the simple harmonic oscillator ground state wavefunction in Q.M.? Is it just that it hasn't been found yet or is it impossible to construct? Also, will the creation and annihilation operators have an explicit differential representation that you can explicitly construct (like for that of the simple harmonic oscillator) or is it not possible?