  We establish an analogy between the Fokker-Planck equation describing
evolutionary landscape dynamics and the Schr\"{o}dinger equation which
characterizes quantum mechanical particles, showing how a population with
multiple genetic traits evolves analogously to a wavefunction under a
multi-dimensional energy potential in imaginary time. Furthermore, we discover
within this analogy that the stationary population distribution on the
landscape corresponds exactly to the ground-state wavefunction. This
mathematical equivalence grants entry to a wide range of analytical tools
developed by the quantum mechanics community, such as the Rayleigh-Ritz
variational method and the Rayleigh-Schr\"{o}dinger perturbation theory,
allowing us to not only make reasonable quantitative assessments but also
explore fundamental biological inquiries. We demonstrate the effectiveness of
these tools by estimating the population success on landscapes where precise
answers are elusive, and unveiling the ecological consequences of
stress-induced mutagenesis -- a prevalent evolutionary mechanism in pathogenic
and neoplastic systems. We show that, even in a unchanging environment, a sharp
mutational burst resulting from stress can always be advantageous, while a
gradual increase only enhances population size when the number of relevant
evolving traits is limited. Our interdisciplinary approach offers novel
insights, opening up new avenues for deeper understanding and predictive
capability regarding the complex dynamics of evolving populations.
