dorsal/arxiv
View SchemaCanonical Transformations and Squeezing in Quantum Mechanics
| Authors | J. M. Cervero, A. Rodriguez-Gonzalez |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0106157 |
| URL | https://arxiv.org/abs/quant-ph/0106157 |
| Journal | International Journal of Theoretical Physics 41, 503-510 (2002) |
Abstract
In this Paper we present an approach to Quantum Mechanical Canonical Transformations. Our main result is that Time Dependent Quantum Canonical Transformations can always be cast in the form of Squeezing Operators. We revise the main properties of these operators in regard to its Lie group properties, how two of them can be combined to yield another operator of the same class and how can also be decomposed and fragmented. In the second part of the paper we show how this procedure works extremely well for the Time Dependent Quantum Harmonic Oscillator. The issue of the systematic construction of Quantum Canonical Transformations is also discussed along the lines of Dirac, Wigner and Schwinger ideas and to the more recent work by Lee. The main conclusion is that the Classical Phase Space Transformation can be maintained in the operator formalism but the construction of the Quantum Canonical Transformation is not clearly related to the Classical Generating Function of a Classical Canonical Transformation. We propose the road of Squeezing Operators rather than the old one attached to Quantum Operators constructed under the guideline of the exponential of the Classical Generating Function.
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"abstract": "In this Paper we present an approach to Quantum Mechanical Canonical\nTransformations. Our main result is that Time Dependent Quantum Canonical\nTransformations can always be cast in the form of Squeezing Operators. We\nrevise the main properties of these operators in regard to its Lie group\nproperties, how two of them can be combined to yield another operator of the\nsame class and how can also be decomposed and fragmented. In the second part of\nthe paper we show how this procedure works extremely well for the Time\nDependent Quantum Harmonic Oscillator. The issue of the systematic construction\nof Quantum Canonical Transformations is also discussed along the lines of\nDirac, Wigner and Schwinger ideas and to the more recent work by Lee. The main\nconclusion is that the Classical Phase Space Transformation can be maintained\nin the operator formalism but the construction of the Quantum Canonical\nTransformation is not clearly related to the Classical Generating Function of a\nClassical Canonical Transformation. We propose the road of Squeezing Operators\nrather than the old one attached to Quantum Operators constructed under the\nguideline of the exponential of the Classical Generating Function.",
"arxiv_id": "quant-ph/0106157",
"authors": [
"J. M. Cervero",
"A. Rodriguez-Gonzalez"
],
"categories": [
"quant-ph"
],
"journal_ref": "International Journal of Theoretical Physics 41, 503-510 (2002)",
"title": "Canonical Transformations and Squeezing in Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0106157"
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