Ground state energies and wave functions of quartic and pure quarticoscillators are calculated by first casting the Schr\"{o}dinger equation into anonlinear Riccati form and then solving that nonlinear equation analytically inthe first iteration of the quasilinearization method (QLM). In the QLM thenonlinear differential equation is solved by approximating the nonlinear termsby a sequence of linear expressions. The QLM is iterative but not perturbativeand gives stable solutions to nonlinear problems without depending on theexistence of a smallness parameter. Our explicit analytic results are thencompared with exact numerical and also with WKB solutions and it is found thatour ground state wave functions, using a range of small to large couplingconstants, yield a precision of between 0.1 and 1 percent and are more accuratethan WKB solutions by two to three orders of magnitude. In addition, our QLMwave functions are devoid of unphysical turning point singularities and thusallow one to make analytical estimates of how variation of the oscillatorparameters affects physical systems that can be described by the quartic andpure quartic oscillators.
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