There exist several ways of making energy-dependent potentials
compatible with standard quantum mechanics. Their brief summaries
may be found, e.g., in refs. [12], [20] or in my own letter ``Linear
representation of energy-dependent Hamiltonians" in Phys. Lett. A
326 (2004) 70 - 76 (quant-ph/0403223)). In paper under review,
Yekken and Lombard add more results in this direction. Among their
most remarkable observations concerning the linearly
energy-dependent forces one finds the discovery of the compression
and saturation of the spectrum or of the difference between the
cases of Coulomb and harmonic-oscillator potentials characterized,
in the latter case, by the failure of finding an equivalent local
potential.

MR2599805 Yekken, R.; Lombard, R. J. Energy-dependent potentials and
the problem of the equivalent local potential. J. Phys. A 43 (2010),
no. 12, 125301, 17 pp. 81Q05 (81P05)