Explain how the expression for the energy levels obtained by solving Klein Gordon equation for a Coulomb field differs from the results derived from Schrödinger equation. Why is this solution not able to explain the fine-structure splitting of the energy levels?
The Klein-Gordon equation describes spin-0 relativistic particles and is given by [ \left[ \frac{1}{c^2} \frac{\partial^2}{\partial t^2} - \nabla^2 + \frac{m^2 c^2}{\hbar^2} \right] \psi = 0 ] For a particle in a Coulomb potential (V(r) = -\frac{Ze^2}{r}), the equation modifies to [ \left[ \left(E - V(r)\right)^2 - (pc)^2 - (mc^2)^2 \right] \psi = 0 ] Solving _________ ____ _________ ___ ________.
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;
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at
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Explain how the expression for the energy levels obtained by solving Klein Gordon equation for a Coulomb field differs from the results derived from Schrödinger equation. Why is this solution not able to explain the fine-structure splitting of the energy levels?
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