Further Difficulties with the Klein-Gordon Equation

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Scientific Paper
Title Further Difficulties with the Klein-Gordon Equation
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Author(s) E Comay
Keywords Relativistic Quantum Mechanics, Dirac Equation, Klein-Gordon Equation, Hamiltonian
Published 2005
Journal Apeiron
Volume 12
Number 1
No. of pages 21

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Herein, the Dirac equation is compared with the Klein-Gordon equation. In contrast to the Dirac case, it is proved that the Klein-Gordon equation has di?culties with the Hamiltonian di?erential operator of relativistic quantum mechanics and with the de?nition of an inner product of wave functions, which is a requirement for a construction of a Hilbert space. An added discussion of the Pauli-Weisskopf article and that of Feshbach-Villars proves that their theories lack a self-consistent expression for the Hamiltonian. Related di?culties are pointed out.