Related papers: Coherent states associated with tridiagonal Hamilt…
We discuss Hamiltonian symmetries and invariants for quantum systems driven by non-Hermitian Hamiltonians. For time-independent Hermitian Hamiltonians, a unitary or antiunitary transformation $AHA^\dagger$ that leaves the Hamiltonian $H$…
The use of the hyperspherical harmonic (HH) basis in the description of bound states in an $A$-body system composed by identical particles is normally preceded by a symmetrization procedure in which the statistic of the system is taken into…
Hamiltonian tridiagonal matrices characterized by multi-fractal spectral measures in the family of Iterated Function Systems can be constructed by a recursive technique here described. We prove that these Hamiltonians are almost-periodic.…
We extend the study of supersymmetric tridiagonal Hamiltonians to the case of non-Hermitian Hamiltonians with real or complex conjugate eigenvalues. We find the relation between matrix elements of the non-Hermitian Hamiltonian $H$ and its…
In a special representation of complex action theory that we call ``future-included'', we study a harmonic oscillator model defined with a non-normal Hamiltonian $\hat{H}$, in which a mass $m$ and an angular frequency $\omega$ are taken to…
A one-to-one correspondence is known to exist between the spectra of the discrete states of the non Hermitian Swanson-type Hamiltonian $ H = {\cal{A}}^{\dagger} {\cal{A}} + \alpha {\cal{A}} ^2 + \beta {\cal{A}}^{\dagger 2} $, ($\alpha \neq…
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product $|z\rangle \langle z|$. Because no pair of coherent states is orthogonal, one…
We introduce creation and annihilation operators of pseudo-Hermitian fermions for two-level systems described by pseudo-Hermitian Hamiltonian with real eigenvalues. This allows the generalization of the fermionic coherent states approach to…
The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…
This work describes coherent states for a physical system governed by a Hamiltonian operator, in two dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential. The…
This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition $H^\dagger=H$ on the Hamiltonian, where $\dagger$ represents the mathematical operation of complex conjugation and matrix…
The Hubbard model is used to study an electronic system. In this paper we present the new path integral representation for Hubbard model. We have constructed the new supercoherent state which appears from a set of eigenfunctions of atomic…
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential equations. The application of the method is based on the…
The nonorthogonality of coherent states is a fundamental property which prevents them from being perfectly and deterministically discriminated. To circumvent this problem, we present an experimentally feasible protocol for the probabilistic…
Coordinate atypical representation of the orthosymplectic superalgebra osp(2/2) in a Hilbert superspace of square integrable functions constructed in a special way is given. The quantum nonrelativistic free particle Hamiltonian is an…
We demonstrate that quantum Hamiltonian operator for a free transverse field within the framework of the second quantization reveals an alternative set of states satisfying the eigenstate functional equations. The construction is based upon…
On the basis of the f-deformed oscillator formalism, we propose to construct nonlinear coherent states for Hamiltonian systems having linear and quadratic terms in the the number operator by means of the two following definitions: i) as…
Using coherent-state representations of quantum mechanics (Bargmann, Husimi, and stellar representations), we describe analytically the phase-space structure of the general eigenstates corresponding to a 1-dimensional bilinear hyperbolic…
States which minimize the Schr\"odinger--Robertson uncertainty relation are constructed as eigenstates of an operator which is a element of the $h(1) \oplus \su(2)$ algebra. The relations with supercoherent and supersqueezed states of the…
The task of analytically diagonalizing a tridiagonal matrix can be considerably simplified when a part of the matrix is uniform. Such quasi-uniform matrices occur in several physical contexts, both classical and quantum, where…