1997/11/17 by Bengt Nagel, Nagel, Bengt · 2 citations
Biochemistry, Genetics and Molecular Biology · Chemistry · Physics and Astronomy · #Electron Spin Resonance Studies #FOS: Physical sciences #Molecular spectroscopy and chirality #Quantum Physics (quant-ph) #Spectroscopy and Quantum Chemical Studies #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9711028
8 p. LaTex. Corrections in eqns (5) and (7)
openalex publication_date 1997/11/17 · arxiv created 1997/12/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.