Exactly solvable energy-dependent potentials

Bohr Hamiltonian with an energy dependent γ-unstable harmonic oscillator potential

“…Thus, considering a harmonic oscillator potential in β shape variable with an energy dependent string constant, v(β, ) = k( )β 2 , one obtains the following equation for the energy of the system [8,13,14]:…”

Modified Darboux transformations with foreign auxiliary equations

“…where the coefficients f and g are given by the following explicit expressions: (11) Note that the indices stand for partial differentiation, as both functions V and H depend on variables other than x. In the next step we convert Eq.…”

“…Therefore, it is important to have methods at hand for finding and generating their solutions. Besides schemes that are based on point transformations, such as in [11], there is a recent result on a very particular type of Darboux transformation [16]. There, a new kind of Darboux transformation for Schrödinger equations with a certain class of energy-dependent potentials is constructed.…”

Exact Solutions of D-Dimensional Klein–Gordon Equation with an Energy-Dependent Potential by Using of Nikiforov–Uvarov Method

“…the Pauli-Schrödinger equation [32,33]. It is noteworthy that in some cases, even if the initial potential is not energy-dependent, its reduction to a wave equation leads to an effective energy-dependent potential [34][35][36][37][38][39]. The harmonic oscillator and linear energy-dependent potentials are examples of analytically-solvable energy-dependent potentials.…”