dorsal/arxiv
View SchemaDisplacement-Operator Squeezed States. I. Time-Dependent Systems Having Isomorphic Symmetry Algebras
| Authors | Michael Martin Nieto, D. Rodney Truax |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9608008 |
| URL | https://arxiv.org/abs/quant-ph/9608008 |
| DOI | 10.1063/1.531836 |
| Journal | J.Math.Phys. 38 (1997) 84-97 |
Abstract
In this paper we use the Lie algebra of space-time symmetries to construct states which are solutions to the time-dependent Schr\"odinger equation for systems with potentials $V(x,\tau)=g^{(2)}(\tau)x^2+g^{(1)}(\tau)x +g^{(0)}(\tau)$. We describe a set of number-operator eigenstates states, $\{\Psi_n(x,\tau)\}$, that form a complete set of states but which, however, are usually not energy eigenstates. From the extremal state, $\Psi_0$, and a displacement squeeze operator derived using the Lie symmetries, we construct squeezed states and compute expectation values for position and momentum as a function of time, $\tau$. We prove a general expression for the uncertainty relation for position and momentum in terms of the squeezing parameters. Specific examples, all corresponding to choices of $V(x,\tau)$ and having isomorphic Lie algebras, will be dealt with in the following paper (II).
{
"annotation_id": "f419c7eb-5707-451a-9859-944729cc4325",
"date_created": "2026-03-02T18:02:37.437000Z",
"date_modified": "2026-03-02T18:02:37.437000Z",
"file_hash": "132c390e8f21dc811f120f05114d0118ad5a1ce7def2ff6497746e4635542af2",
"private": false,
"record": {
"abstract": "In this paper we use the Lie algebra of space-time symmetries to construct\nstates which are solutions to the time-dependent Schr\\\"odinger equation for\nsystems with potentials $V(x,\\tau)=g^{(2)}(\\tau)x^2+g^{(1)}(\\tau)x\n+g^{(0)}(\\tau)$. We describe a set of number-operator eigenstates states,\n$\\{\\Psi_n(x,\\tau)\\}$, that form a complete set of states but which, however,\nare usually not energy eigenstates. From the extremal state,\n $\\Psi_0$, and a displacement squeeze operator derived using the Lie\nsymmetries, we construct squeezed states and compute expectation values for\nposition and momentum as a function of time, $\\tau$. We prove a general\nexpression for the uncertainty relation for position and momentum in terms of\nthe squeezing parameters. Specific examples, all corresponding to choices of\n$V(x,\\tau)$ and having isomorphic Lie algebras, will be dealt with in the\nfollowing paper (II).",
"arxiv_id": "quant-ph/9608008",
"authors": [
"Michael Martin Nieto",
"D. Rodney Truax"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.531836",
"journal_ref": "J.Math.Phys. 38 (1997) 84-97",
"title": "Displacement-Operator Squeezed States. I. Time-Dependent Systems Having Isomorphic Symmetry Algebras",
"url": "https://arxiv.org/abs/quant-ph/9608008"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "cbc465b0-5caa-4464-8858-455e6bb3d61d",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}