Terahertz (THz) waves can be generated by the nonlinear interaction between ultrashort laser pulses and air. The semiclassical photocurrent model is widely used. It is simple, but neglects the quantum effects. Some theoretical works are based on solving the time-dependent Schrödinger equation. However, it meets the difficulty of prohibitively large boxes in long-time evolution. Here we adopted the wave-function splitting algorithm to fully contain the information of photoelectrons. The contributions of the excited states and interference effects in electron wavepackets to THz radiation are studied numerically. We also theoretically investigated the THz generation from nitrogen molecules in a biased electric field. It is found that the THz yield enhancement as a function of the static field strength in experiments can be reproduced well by our method. In addition, the restriction of wavelength and phase difference in the two-color laser fields is less strict in the presence of the static field.