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Consider two operators A = B. Whenever one divides both sides of the equation by a variable r which can also take on the value zero, one should add on to one side an arbitrary multiple of δ(r), that is, 1/r A = 1/r B + aδ(r) where a is an unknown c number. See, Dirac P A M 1958 The Principles of Quantum Mechanics 4th edn (Oxford: Clarendon) p 61
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