STUDY OF QUANTUM ANHARMONIC-OSCILLATORS BY STATE-DEPENDENT DIAGONALIZATION

In the present work, we propose the method of state-dependent diagonal ization to find the energy eigenvalues and eigenstates of a quantum an harmonic oscillator. The example of a cubic-quartic anharmonic oscilla tor is used to illustrate its validity. Unlike the conventional exact diagonalization, this method is shown to be very efficient for calcula ting the energy eigenvalues of the excited states as well as the corre sponding eigenfunctions. That is, no huge matrix needs to be diagonali zed in this approach.