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An operator relating the past asymptotic state of a dynamical system governed by the Schrödinger equation id/(dt)psi(t)=Hpsi(t) to its future asymptotic state.

An operator relating the asymptotic state of a dynamical system governed by the Schrödinger equation ihd/(dt)psi(t)=Hpsi(t) to its original asymptotic state.

A second-order linear Hermitian operator is an operator L^~ that satisfies int_a^bv^_L^~udx=int_a^buL^~v^_dx. (1) where z^_ denotes a complex conjugate. As shown in ...

The operator I^~ which takes a real number to the same real number I^~r=r.

An operator T which maps some basic polynomial sequence p_n(x) into another basic polynomial sequence q_n(x).

A linear operator A:D(A)->H from its domain D(A) into a Hilbert space H is closable if it has a closed extension B:D(B)->H where D(A) subset D(B). Closable operators are ...

If V and W are Banach spaces and T:V->W is a bounded linear operator, the T is said to be a compact operator if it maps the unit ball of V into a relatively compact subset of ...

The operator representing the computation of a derivative, D^~=d/(dx), (1) sometimes also called the Newton-Leibniz operator. The second derivative is then denoted D^~^2, the ...

The operator D=-i(d+d^*), where d^* is the adjoint.

Let T be a linear operator on a separable Hilbert space. The spectrum sigma(T) of T is the set of lambda such that (T-lambdaI) is not invertible on all of the Hilbert space, ...