由洛伦兹变换产生的自由薛定谔方程的一类旅行包络解
A class of traveling-envelope solutions of free Schrödinger equation generated by Lorentz transformation
摘要：
本文给出了一类振幅以常群速度运动而形状不变的自由粒子的薛定谔方程的行波包络解。证明了当量子平均能量$E$和动量$p$与粒子的静止质量$m$之间有爱因斯坦公式$E^2/c^2-p^2=m^2c^2$关系时，任意有限群速度的解都可以通过Lorentz推升群速度为零的解得到.的波函数是空间本地化的有限尺寸的支持，这是减少的静止质量和/或群速度的增加。对于静止质量为零但动量有限的粒子，我们证明了群速度和相速度等于光速，波长由爱因斯坦的另一个公式$λ_P=h/p$给出.
英文摘要：
We develop a class of traveling-envelope solutions of Schrödinger equation for a free particle whose amplitude is moving with constant group velocity while keeping its shape undistorted. We show that solution with arbitrary finite group velocity is obtained by Lorentz boosting the solution with vanishing group velocity, if the quantum average energy $E$ and momentum $p$ are related to the rest-mass $m$ of the particle by Einstein formula $E^2/c^2-p^2=m^2c^2$. The wave function is spatially localized with finite-size support which is decreasing as the rest-mass and/or group velocity are increased. For a particle with vanishing rest-mass yet finite momentum, we show that the group and phase velocities are equal to the velocity of light and the wavelength is given by Einstein another formula $λ_P=h/p$.
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