Reconciling relativity and quantum mechanics

We would like to express the kinetic energy Ejdn through the particle s momentum p, because we would then know how to obtain the corresponding quantum mechanical operators (Chapter 1, p. 18). To this end let us consider the expression 

F fninan, RJi. Leighton, M. Sands, Feynnum Lectures on Phystcs , Addison-Wesley Publishing Company, 1964. 

If we wanted to use the last expression to construct the Hamiltonian, then we would find serious difficulty, namely, the momentum operator p = —ihV (replacing p according to the appropriate postulate. Chapter 1) is under the square root sign, thus leading to non-linear operators. Brave scientists noted, however, that if you squared both sides, the danger would disappear. We would obtain 

All this has been, and still is, a sort of groping and guessing from some traces or indications. 

The equations corresponding to physical quantities will be transformed to the corresponding operator equations, and it will be assumed that both sides of them will act on a wavefunction. 

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