A new version of solutions in the form of an exponentially weighted power series is constructed for the two-dimensional circularly symmetric quartic oscillators, which reflects successfully the desired properties of the exact wave function. The regular series part is shown to be the solution of a transformed equation. The transformed equation is applicable to the one-dimensional problem as well. Moreover, the exact closed-form eigenfunctions of the harmonic oscillator can be reproduced as a special case of the present wave function.
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H. Ta eli (1996) studied this question.
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