  By exactly solving the effective two-body interaction for two-dimensional
electron system with layer thickness and an in-plane magnetic field, we
recently found that the effective interaction can be described by the
generalized pseudopotentials (PPs) without the rotational symmetry. With this
pseudopotential description, we numerically investigate the behavior of the
fractional quantum Hall (FQH) states both in the lowest Landau level (LLL) and
first Landau level (1LL). The enhancements of the 7/3 FQH state on the 1LL for
a small tilted magnetic field are observed when layer thickness is larger than
some critical values. While the gap of the 1/3 state in the LLL monotonically
reduced with increasing the in-plane field. From the static structure factor
calculation, we find that the systems are strongly anisotropic and finally
enter into a stripe phase with a large tilting. With considering the Landau
level mixing correction on the two-body interaction, we find the strong LL
mixing cancels the enhancements of the FQH states in the 1LL.
