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- W2119625144 abstract "A new type of basis set for quantum mechanical problems is introduced. These basis states are adapted to describing the dynamics of a Hamiltonian Ĥ which is dependent upon a parameter X. A function f(E) is defined which is an analytic function of E, and which is negligibly small when |E|>>δE, where δE is large compared to the typical level separation. The energy-shell basis set consists of states |ξn(X)⟩ which are derived by applying the operator f(Ĥ(X)-Ēn(X)) to elements of a fixed basis set, where Ēn(X) is an analytic approximation to an eigenvalue En(X). The energy-shell basis states are combinations of states close to energy En, but vary more slowly as a function of X than the eigenfunctions |ϕn(X)⟩ of Ĥ(X). This feature gives the energy-shell basis states some advantages in analysing solutions of the time-dependent Schrödinger equation." @default.
- W2119625144 created "2016-06-24" @default.
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- W2119625144 date "2001-12-05" @default.
- W2119625144 modified "2023-09-27" @default.
- W2119625144 title "Energy-shell bases" @default.
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- W2119625144 doi "https://doi.org/10.1088/0305-4470/34/49/328" @default.
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