We investigate the transmission coefficient of an electron through a quantum point contact (QPC) in a tilted magnetic field and a crossed electric field. It is found that the widely employed model by Fertig and Halperin (FH) (1987) [20] is only defined when the sum of squares of oscillator strengths of parabolic QPC confinement and magnetic field in transverse direction exceeds that of QPC antibounding (repulsing) potential along the transport direction (${\mathrm{\Omega }}^2>0$). We therefore extend the FH model to the case when the parameters do not satisfy this condition (${\mathrm{\Omega }}^2<0$), and propose a different unitary transformation to obtain the corresponding analytical expression for the transmission coefficient. The electric and magnetic effects on the transmission coefficient are discussed. As an example of application, we also investigate the magnetic effects on the constriction conductance for the extended model in the absence of the electric fields. In contrast to the well-defined quantization in the FH model, it is shown that the constriction conductance for the extended model could have well-defined, poor, or even no quantization.

我们研究了电子在倾斜磁场和交叉电场中通过量子点接触 (QPC) 的传输系数。发现 Fertig 和 Halperin (FH) (1987) [20] 广泛采用的模型仅在抛物线 QPC 约束和横向磁场的振荡器强度平方和超过 QPC 反边界（排斥）时才定义沿传输方向的电势（${\mathrm{\Omega }}^2>0$）。因此，我们将 FH 模型扩展到参数不满足此条件的情况（${\mathrm{\Omega }}^2<0$)，并提出不同的幺正变换以获得相应的透射系数解析表达式。讨论了电和磁对传输系数的影响。作为应用示例，我们还研究了在没有电场的情况下对扩展模型的收缩电导的磁效应。与 FH 模型中明确定义的量化相比，扩展模型的收缩电导可能具有明确定义、较差甚至没有量化。