Study of quantum anharmonic oscillators by state-dependent diagonalization

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Abstract
In the present work, we propose the method of state-dependent diagonalization to find the energy eigenvalues and eigenstates of a quantum anharmonic oscillator. The example of a cubic-quartic anharmonic oscillator is used to illustrate its validity. Unlike the conventional exact diagonalization, this method is shown to be very efficient for calculating the energy eigenvalues of the excited states as well as the corresponding eigenfunctions. That is, no huge matrix needs to be diagonalized in this approach. © 1996 The American Physical Society.