Abstract
A generalized Neumann hierarchy is obtained by restricting the hierarchy of integrable evolution equations associated with the energy dependent Schrödinger equation to the invariant subspace of its recursion operator. The integrals of motion and Hamiltonian functions for this hierarchy are constructed by using a recursion formula related to the eigenvalue problem. The generalized Neumann systems are shown to be completely integrable and to commute with each other. This provides a way to solve the evolution equation.
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