We have generalized the plane-wave method used by Mathine et al (Mathine D L, Myjak S K and Maracas G N 1995 IEEE J. Quantum Electron. 31 1216-22) for electrons to the case of light and heavy holes in quantum well systems with an arbitrary growth direction. Our method allows for relaxing the assumption of constant Luttinger parameters as used by Xia (Xia J-B 1991 Phys. Rev. B 43 9856-64) and remains valid when the parameters experience discontinuities across the heterointerface. Although the method has been thoroughly tested for rectangular quantum wells only, it can be equally well applied to quantum wells of other shapes also.