浅议导出玻尔量子化条件的驻波条件

A Tentative Study of Standing Wave Condition Used to Deduce Bohr Quantized Condition

从教科书中根据直线弦振动的驻波条件,处理电子绕核作圆周运动角动量的量子化问题,导致了与玻尔理论量子化条件不一致的结论。提出利用驻波的特点和封闭弦振动驻波满足的对称性,得出圆形封闭弦形成驻波的条件为周长是半波长的偶数倍。利用此条件可以处理电子绕核作圆周运动的角动量量子化问题,从而得出与玻尔定态理论一致的结论。最后把玻尔定态理论的3个假设分别与驻波特点相对应,用驻波的特性解释了电子绕核运动的能量、角动量的量子化问题。

This paper thinks that the conclusion will disagree with the Bohr angular momentum quantized condition, if the standing wave condition of linear string vibration is used directly to deal with angular momentum of the motion of electron going round nucleus in a circle in the textbook. The paper holds that if one employs the character of the standing wave and the symmetry satisfied by standing wave condition of circinal string vibration, he can reach that the condition of the standing wave of circinal string vibration is just the circumference of the circle equal to even times of half of the wavelength. Through that condition, one can obtain the quantized angular momentum consistent with the stationary state of Bohr Theory. At the end of the paper the authors explain the quantized angular momentum and the quantized energy with the character of the standing wave.