ABSTRACT

H R W R y y( ) ( )= (11.15) This system is the general case of a stationary state. This equation is also called the eigenvalue equation in which W is the eigenvalue of the system (constant) and y is the eigenfunction (wavefunction). If a possible value of observable A is defined as · Ò = =ÚA R t A R t dR R t A R tY Y Y Y* *( , ) ( , ) ( , ) ( , ) (11.16)substituting Eq. 11.16 in Eq. 11.15, we get A R t A R e iWt Y System

( , ) ( )= · ÒÂ -y (11.17) Next, if the Hamiltonian operator is separated into unperturbed and perturbation parts as H H H = +0 ¢ (11.18) we will finally have a solution to the energy W and the wavefunction y as W W m H m k H m

= + + -

+ π ¢

¢ 2 (11.19)

m k k H m

W W = +

- +

π Â ¢ (11.20)

11.3 Semi-Classical Quantum Mechanical TreatmentHere we will determine the dielectric response of matter under the light frequency by solving a time-dependent perturbation theory (Fig. 11.2).