I didn't find in literature K-G eq. for non-free particle. Anybody who knows please write me down it.
Thanks in advance
Viktor
What do you mean by potential field? Need to be carefull with the expressions before asking questions.
Any field discribed by scalar potential energy U(q) to add in proper way into Hamiltonian. Say harmonic oscillator U(q)=wq^2/2
Best regards
V.Ch.
Check the book of Greiner named "Relativistic Quantum Mechanis:Wave equations""
As is always the case, the equation of motion is obtained by the variation of the action; for the case at hand, Box φ + V'(φ) = 0, where Box is the d'Alembertian operator. The quadratic part of V is the mass term and the non-quadratic the interaction. The reason is that the most general action, consistent with Lorentz invariance, and containing two derivatives of the scalar field, is the spacetime integral of -(1/2)φ(Box φ) -V(φ), where V(.) is a Lorentz scalar function of φ(x) (up to a total derivative term). The Klein-Gordon equation is the equation of the field, whose excitations are particles.
Lol. The usual procedure in quantum mechanics is to replace derivatives with derivative -eA, where A is a component of the 4-vector defining the external field.
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