Transition of the Heisenberg equation for $h\to 0$ to the dynamic equation of a monoatomic ideal gas and quantization of relativistic hydrodynamics

It is shown that the equation $h^2\square\psi+k^2\psi^{7/3}=0$ for $h\to 0$ transforms into a system of dynamic equations of a monoatomic ideal gas ($c_v =3/2$), and the equation $h^2\square\psi+k^2|\psi|^2\psi=0$ for $h\to 0$ transforms into a system of dynamic equations of a monoatomic ideal gas ($c_v =1$).