相关论文: Energy-dependent Hamiltonians and their pseudo-Her…
The calculation of ground-state energies of physical systems can be formalised as the k-local Hamiltonian problem, which is the natural quantum analogue of classical constraint satisfaction problems. One way of making the problem more…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
An exact analytical solution for the Bohr Hamiltonian with an energy dependent Coulomb-like $\gamma$-unstable potential is presented. Due to the linear energy dependence of the potential's coupling constant, the corresponding spectrum in…
We consider on a symplectic manifold M with Poisson bracket {,} an Hamiltonian H with complete flow and a family Phi=(Phi_1,...,Phi_d) of observables satisfying the condition {{Phi_j,H},H}=0 for each j. Under these assumptions, we prove a…
Schroedinger equation on a Hilbert space ${\cal H}$, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space $P {\cal H}$. Separable states of a bipartite quantum system form a…
Although energy levels are often given by solutions of the radial equation such that u(0) is non zero, and hence by first-order singular functions which are not eigenfunctions of H, the latter is always considered as the only operator that…
For two self-adjoint operators $H,A$ we show that a general commutation relation of type $[H,\mathrm{i}A]=Q(H)+K$, in addition to regularity of $H$ and Kato-smoothness of $K$, guarantee pointwise in time decay rates of diverse order. The…
It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of…
This paper deals with the mathematical spectral analysis and physical interpretation of a fermionic system described by a non-Hermitian Hamiltonian possessing real eigenvalues. A statistical thermodynamical description of such a system is…
We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of…
We consider quantum systems which interact strongly with a rapidly varying environment and derive a Schrodinger-like equation which describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be…
Within this article one finds the statement of the Klein-Gordon problem within the real Hilbert space formalism ($\mathbbm R$HS) in terms of complex wave functions, and in terms of quaternionic wave functions as well. The complex…
We recently introduced a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics…
The current applications of non-Hermitian but ${\cal PT}-$symmetric Hamiltonians $H$ cover several, mutually not too closely connected subdomains of quantum physics. Mathematically, the split between the open and closed systems can be…
Interacting and open quantum systems can be formulated in terms of an effective non-Hermitian Hamiltonian (NHH), however, there are important constraints that must be satisfied by the effective action and the associated Green's functions.…
The additional information within a Hamilton-Jacobi representation of quantum mechanics is extra, in general, to the Schr\"odinger representation. This additional information specifies the microstate of $\psi$ that is incorporated into the…
It is shown that the eigenvalue problem for the Hamiltonians of the standard form, $H=p^2/(2m)+V(x)$, is equivalent to the classical dynamical equation for certain harmonic oscillators with time-dependent frequency. This is another…
We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in…
I point out that if one defines the operator $U_R(t)$ as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of $U_R(t)$ as given in his paper…
The spectral analysis of a non-Hermitian unbounded operator appearing in quantum physics is our main concern. The properties of such an operator are essentially different from those of Hermitian Hamiltonians, namely due to spectral…