Coherent-Squeezed State Representation of Travelling General Gaussian Wave Packets
Coherent-Squeezed State Representation of Travelling General Gaussian Wave Packets
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行进的一般高斯波包的相干压缩状态表示
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发表时间：
2005
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通讯作者：
Sang Pyo Kim
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作者：
Sang Pyo Kim
利用含时不变的湮灭算符和产生算符，对于自由质量和振子，我们找到了具有位置和动量的初始期望值x_0和p_0以及方差Δ x_0和Δ p_0的一般高斯波包的相干压缩态表象。初始的一般高斯波包在归一化因子下采用形式$e^{ip_0 x/hbar} e^{-（1 mp i delta）（x - x_0）^2 / 4（Delta x_0）^2}$，其中$delta = sqrt{（2 Δ x_0 Δ p_0/hbar）^2 - 1}$表示与最小不确定性或初始位置-动量相关性的偏差的度量。2Delta（xp）_0 / hbar$。行进的高斯波包在相位和归一化因子与时间相关的情况下采用形式$e^{ip_c x/hbar} e^{-（1 - 2 i Delta（xp）_t/hbar）（x-x_c）^2 / 4（Delta x_t）^2}$，并且质心遵循经典轨迹$x_c（t）$和$p_c（t）$。的位置方差被发现有另外一个线性的时间依赖项与$delta$成正比，正负符号。
Using the time-dependent annihilation and creation operators, the invariant operators, for a free mass and an oscillator, we find the coherent-squeezed state representation of a travelling general Gaussian wave packet with initial expectation values, $x_0$ and $p_0$, of the position and momentum and variances, $Delta x_0$ and $Delta p_0$. The initial general Gaussian wave packet takes, up to a normalization factor, the form $e^{i p_0 x/hbar} e^{- (1 mp i delta) (x - x_0)^2 / 4 (Delta x_0)^2}$, where $delta = sqrt{(2Delta x_0 Delta p_0/hbar)^2 -1}$ denotes a measure of deviation from the minimum uncertainty or the initial position-momentum correlation $delta = 2Delta (xp)_0 / hbar$. The travelling Gaussian wave packet takes, up to a time-dependent phase and normalization factor, the form $e^{i p_c x/hbar} e^{- (1 - 2 i Delta (xp)_t/hbar) (x - x_c)^2 / 4 (Delta x_t)^2}$ and the centroid follows the the classical trajectory with $x_c(t)$ and $p_c(t)$. The position variance is found to have additionally a linearly time-dependent term proportional to $delta$ with both positive and negative signs.