Preferred Label : perturbation theory;
IUPAC definition : Along with variational method, the second major quantum-mechanical approximation method.
The methods of perturbation theory are based on representation of the Hamiltonian
of a system under study, H, through the Hamiltonian, H0, of a system, whose Schroedinger
equation is solvable, and its relatively small perturbation H': H H0 H'. Numerous
techniques are derived allowing one to relate the unknown eigenvalues and eigenfunctions
of the perturbed system to the known eigenvalues and eigenfunctions of the unperturbed
system. As distinct from the variational method, the methods of perturbation theory
are applicable to all the electronic states of an atom or molecule. When H' is time-dependent,
the perturbed system does not have stationary states. In this case time-dependent
perturbation theory, which is the method of approximate calculation of the expansion
of wave-functions of the perturbed system over wave-functions of stationary states
of the unperturbed system, must be employed. The applications of this method are associated
mostly with studies of light emission and absorption by atoms and molecules.;
Origin ID : PT07090;
See also
Along with variational method, the second major quantum-mechanical approximation method.
The methods of perturbation theory are based on representation of the Hamiltonian
of a system under study, H, through the Hamiltonian, H0, of a system, whose Schroedinger
equation is solvable, and its relatively small perturbation H': H H0 H'. Numerous
techniques are derived allowing one to relate the unknown eigenvalues and eigenfunctions
of the perturbed system to the known eigenvalues and eigenfunctions of the unperturbed
system. As distinct from the variational method, the methods of perturbation theory
are applicable to all the electronic states of an atom or molecule. When H' is time-dependent,
the perturbed system does not have stationary states. In this case time-dependent
perturbation theory, which is the method of approximate calculation of the expansion
of wave-functions of the perturbed system over wave-functions of stationary states
of the unperturbed system, must be employed. The applications of this method are associated
mostly with studies of light emission and absorption by atoms and molecules.
