An analogous phenomenon to predator prey population dynamics in quantum mechanics is also appreciated.
the answer is a plain no. i think that predator prey equations are deterministic and does not involve quantum mechanical operators.
To the extent that Lotk-Volterra systems are Hamiltonian, that Hamiltonian can be quantised. But that does not mean, of course, that the corresponding system has anything to do with ``a quantum version'' of predator-prey interaction.
This touches maybe slightly more general topic. Some equations in QM are formally very similar to classic equations (e.g. Schrodinger vs Heat equation). One could then think that maybe for example Black-Scholes option pricing equation, which is also based on Heat equation, could find its quantum counterpart. Of course, formally. But the key aspect is the physical interpretation and motivation for introduction of such equation. I think that this could be the same problem of quantum L-V equation.
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