The Born Oscillator

The paper studies the properties of an oscillator whose Hamiltonian is $[(1+q^2)(1+p^2){]}^{1\mathrm{/}2}-1$. It can be deduced from the nonlinear theory of electrodynamics originally proposed by Max Born in 1934. The quantization of such oscillator represents a possible regularization of the Barry and Keating’s Hamiltonian, which has been proposed in the framework of the theory of non-trivial zeros of the Riemann’s $\zeta$ function.