A new kind of κ-quantum nonlinear coherent states:: Their generation and physical meaning

A new kind of k-quantum nonlinear coherent states, i.e., the k eigenstates of the k-th power B-k (k greater than or equal to 3) of the generalized annihilation operator B = a1/f(N) of f-oscillators, are obtained and their properties are discussed. The completeness of the k states is investigated. An alternative method to construct them is proposed. It is shown that these states may form a complete Hilbert space, and all of them can be generated by a linear superposition of k Roy-type nonlinear coherent states. Physically, they can be generated by a linear superposition of the time-dependent Roy-type nonlinear coherent states at different instants.