  Based on a parametrization of pure quantum states we explicitly construct a
sequence of (at most) $4N-5$ local time-continuous waveform controls to achieve
a specified state transition for $N$-level quantum systems when sufficient
controls of the Hamiltonian are available. The control magnitudes are further
optimized in terms of a time-energy performance, which is a generalization of
the time performance index. Trajectory-constrained optimal local
time-continuous waveform controls, including both local sine-waveforms and
$n^{\rm th}$-order-polynomial waveform controls are obtained in terms of
time-energy performance. It is demonstrated that constrained optimal local
$n^{\rm th}$-order-polynomial waveform controls approach constrained optimal
bang-bang controls when $n\rightarrow\infty$.
