Higher power squeezed states, Jacobi matrices, and the Hamburger moment problem
| dc.creator | Nagel, Bengt | |
| dc.date | 1997-11-17 | |
| dc.date | 1997-12-02 | |
| dc.date.accessioned | 2026-07-07T06:14:33Z | |
| dc.date.available | 2026-07-07T06:14:33Z | |
| dc.description | k:th power (amplitude-)squeezed states are defined as the normalized states giving equality in the Schroedinger-Robertson uncertainty relation for the real and imaginary parts of the k:th power of the one-mode annihilation operator. Equivalently they are the set of normalized eigenstates (for all possible complex eigenvalues) of the Bogolubov transformed "k:th power annihilation operators". Expressed in the number representation the eigenvalue equation leads to a three term recursion relation for the expansion coefficients, which can be explicitly solved in the cases k = 1, 2. The solutions are essentially Hermite and Pollaczek polynomials, respectively. k = 1 gives the ordinary squeezed states, i.e. displaced squeezed vacua. For k equal to or larger than three, where no explicit solution has been found, the recursion relation for the symmetric operator given by the real part of the k:th power of the annihilation operator defines a Jacobi matrix corresponding to a classical Hamburger moment problem, which is undetermined. This implies that the operator has an infinity of self-adjoint extensions, all with disjoint discrete spectra. The corresponding squeezed states are well-defined, however. | |
| dc.description | 8 p. LaTex. Corrections in eqns (5) and (7) | |
| dc.identifier | https://arxiv.org/abs/quant-ph/9711028 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/9711028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/93502 | |
| dc.subject | Quantum Physics | |
| dc.title | Higher power squeezed states, Jacobi matrices, and the Hamburger moment problem | |
| dc.type | text |