Classical Representation for Quantum States of a Particle in $λ z^{2m}$ potential

• URL: http://arxiv.org/abs/2510.18809v1
• Date: Tue, 21 Oct 2025 17:04:31 GMT
• Title: Classical Representation for Quantum States of a Particle in $λ z^{2m}$ potential
• Authors: Tasko Grozdanov, Evgeni Solov'ev,
• Abstract summary: A classical representation for quantum eigenstates of a particle bound in $lambda z2m$ $(lambda >0, m=1,2,...)$ potentials is developed.<n>The corresponding Schr"odinger equation in classical representation is analyzed.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A classical representation for quantum eigenstates of a particle bound in $\lambda z^{2m}$ $(\lambda >0, m=1,2,...)$ 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 Schr\"odinger equation in classical representation is analyzed.

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