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Nuclear Physics in a Nutshell by Carlos A. Bertulani

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Appendix D Relativistic Quantum Mechanics

D.1 Lagrangians

For discrete systems the Hamilton principle yields the Lagrangian equations

Image

where the Lagrangian is the difference between the kinetic energy and the potential energy, i.e.L = TV. The Hamiltonian is given by Image, where Image.

If ηi is the displacement of particle i from its equilibrium position (see figure D.1), then

where a is the separation distance between the equilibrium positions of two neighboring ...

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