The rigged Hilbert spaces (RHS) are the right mathematical context which includes many tools used in quantum physics, or even in some chaotic classical systems. It is particularly interesting that in RHS coexist discrete and continuous basis, abstract basis along basis of special functions and representations of Lie algebras of symmetries by continuous operators. This is not possible in Hilbert spaces. In the present paper, we study a model showing all these features, based on the one dimensional P\"oschl-Teller Hamiltonian. Also, RHS support representations of all kinds of ladder operators as continuous mappings. We give an interesting example based on one dimensional Hamiltonians with an infinite chain of SUSY partners, in which the factorization of Hamiltonians by continuous operators on RHS plays a crucial role.