DOI link for APPROXIMATION METHODS
APPROXIMATION METHODS book
We have seen that to determine the possible energies En (energy eigenvalues) which a physical system can have and the corresponding eigenfunctions (wave functions) ψn, we have to set up and solve the time-independent Schro¨dinger equation
Hψn = Enψn . (8.1.1)
In this equation, the wave function ψn, representing the n-th eigenstate of the system in the coordinate representation, is a function of the continuously varying eigenvalues of the position observables of the system, the number of position observables being equal to number of degrees of freedom of the system. The Hamiltonian operator H, in the coordinate representation, is a differential operator involving the continuously varying eigenvalues of the position observables and the derivatives with respect to them. Since we will be dealing with the operators mostly in the coordinate representation, we shall denote them without the caret.