Classical Representation for Quantum States of a Particle in $λz^{2m}$ potential
A classical representation for quantum eigenstates of a particle bound in $λz^{2m}$ $(λ>0, m=1,2,...)$ potentials is developed. It is represented by ensembles of classical trajectories with energy distributions that can take on negative values, for $m>1$ have integrable singularities at zero energy and whose mean energies coincide with quantum eigenenergies. The corresponding Schrödinger equation in classical representation is analyzed.
quant-ph↗