  The accuracy of different transfer matrix approaches, widely used to solve
the stationary effective mass Schr\"{o}dinger equation for arbitrary
one-dimensional potentials, is investigated analytically and numerically. Both
the case of a constant and a position dependent effective mass are considered.
Comparisons with a finite difference method are also performed. Based on
analytical model potentials as well as self-consistent Schr\"{o}dinger-Poisson
simulations of a heterostructure device, it is shown that a symmetrized
transfer matrix approach yields a similar accuracy as the Airy function method
at a significantly reduced numerical cost, moreover avoiding the numerical
problems associated with Airy functions.
