dorsal/arxiv
View SchemaCoherent-Squeezed State Representation of Travelling General Gaussian Wave Packets
| Authors | Sang Pyo Kim |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511073 |
| URL | https://arxiv.org/abs/quant-ph/0511073 |
| Journal | J. Korean Phys. Soc. 49 (2006) 464-471 |
Abstract
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 $\delta = \sqrt{(2\Delta x_0 \Delta p_0/\hbar)^2 -1}$ denotes a measure of deviation from the minimum uncertainty or the initial position-momentum correlation $\delta = 2\Delta (xp)_0 / \hbar$. 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.
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"abstract": "Using the time-dependent annihilation and creation operators, the invariant\noperators, for a free mass and an oscillator, we find the coherent-squeezed\nstate representation of a travelling general Gaussian wave packet with initial\nexpectation values, $x_0$ and $p_0$, of the position and momentum and\nvariances, $\\Delta x_0$ and $\\Delta p_0$. The initial general Gaussian wave\npacket takes, up to a normalization factor, the form $e^{i p_0 x/\\hbar} e^{- (1\n\\mp i \\delta) (x - x_0)^2 / 4 (\\Delta x_0)^2}$, where $\\delta = \\sqrt{(2\\Delta\nx_0 \\Delta p_0/\\hbar)^2 -1}$ denotes a measure of deviation from the minimum\nuncertainty or the initial position-momentum correlation $\\delta = 2\\Delta\n(xp)_0 / \\hbar$. The travelling Gaussian wave packet takes, up to a\ntime-dependent phase and normalization factor, the form $e^{i p_c x/\\hbar} e^{-\n(1 - 2 i \\Delta (xp)_t/\\hbar) (x - x_c)^2 / 4 (\\Delta x_t)^2}$ and the centroid\nfollows the the classical trajectory with $x_c(t)$ and $p_c(t)$. The position\nvariance is found to have additionally a linearly time-dependent term\nproportional to $\\delta$ with both positive and negative signs.",
"arxiv_id": "quant-ph/0511073",
"authors": [
"Sang Pyo Kim"
],
"categories": [
"quant-ph"
],
"journal_ref": "J. Korean Phys. Soc. 49 (2006) 464-471",
"title": "Coherent-Squeezed State Representation of Travelling General Gaussian Wave Packets",
"url": "https://arxiv.org/abs/quant-ph/0511073"
},
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