  The analytical transfer matrix technique is applied to the Schr\"{o}dinger
equation of symmetric quartic-well potential problem in the form
$V(x)={1/2}kx^{2}+\lambda{x^{4}}.$ This gives quantization condition from which
we can calculate the ground-state energy eigenvalues numerically. We also
compare the results with those obtained from numerical shooting method,
perturbation theory, and WKB method.
