Question

B2 (a) Derive the Klein-Gordon equation (in S.I. units) starting from the energy-momentum relationship, E2 -mc4+kc2 using the quantum mechanical relations [3 Marks] (b) Write this in natural units [2 Marks] (c) Using the expression for the Laplacian in the radially symmetric case 8(3) r2 a show that the solution of the Klein-Gordon equation in the static case is (re-/R where R 1/m. You may wish to use the substitution [8 Marks] (d) Using the Heisenberg Uncertainty Principle, show that a particle of mass m will have a typical range R, which is the same as that derived in part (c) [5 Marks] (e) Explain what these results say about the form of the electromagnetic potential and its range. [2 Marks]

Answer 1

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