Related papers: Self-adjoint Time Operator is the Rule for Discret…

Let $H$ be a complex Hilbert space and let ${\mathcal C}$ be a conjugacy class of finite rank self-adjoint operators on $H$ with respect to the action of unitary operators. We suppose that ${\mathcal C}$ is formed by operators of rank $k$…

To admit a canonically conjugate time operator, the Hamiltonian has to be a generator of translations (like the momentum operator generates translations in space), so its spectrum must be unbounded. But the Hamiltonian governing our world…

Within the framework of self-adjoint operator of time in non-relativistic quantum mechanics some properties of solutions of Schroedinger equation, related to Hilbert space formalism, are investigated for two types of time dependent…

We consider a class of (possibly nondiagonalizable) pseudo-Hermitian operators with discrete spectrum, showing that in no case (unless they are diagonalizable and have a real spectrum) they are Hermitian with respect to a semidefinite inner…

Let $T$ be a densely defined closed symmetric operator with equal deficiency indices in a separable complex Hilbert space $H$. In this paper, we prove that $T$ has a self-adjoint extension with compact resolvent if and only if the domain…

We give an explicit description of all minimal self-adjoint extensions of a densely defined, closed symmetric operator in a Hilbert space with deficiency indices $(1, 1)$.

In [J. Math. Phys. 51 (2010) 022104] a self-adjoint operator was introduced that has the property that it indicates the direction of time within the framework of standard quantum mechanics, in the sense that as a function of time its…

In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.

Let $H$ be a complex Hilbert space of dimension not less than $3$ and let ${\mathcal C}$ be a conjugacy class of compact self-adjoint operators on $H$. Suppose that the dimension of the kernels of operators from ${\mathcal C}$ not less than…

We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…

Using the Spectral Theorem for unbounded self-adjoint operators we prove that any countable family of Lagrangian subspaces of a symplectic Hilbert space admits a common complementary Lagrangian.

We provide sufficient and necessary conditions guaranteeing equations $(A+B)^*=A^*+B^*$ and $(AB)^*=B^*A^*$ concerning densely defined unbounded operators $A,B$ between Hilbert spaces. We also improve the perturbation theory of selfadjoint…

For classical dynamical systems time operators are introduced as selfadjoint operators satisfying the so called weak Weyl relation with the unitary groups of time evolution. Dynamical systems with time operators are intrinsically…

We define a second-order differential operator $\hat{C}$ on the Hilbert space $L^2([-v_c, v_c])$, constructed from a smooth deformation function $C(v)$. The operator is considered on the Sobolev domain $H^2([-v_c, v_c]) \cap H^1_0([-v_c,…

It is shown that in presence of certain external fields a well defined self-adjoint time operator exists, satisfying the standard canonical commutation relations with the Hamiltonian. Examples include uniform electric and gravitational…

We produce a simple criterion and a constructive recipe to identify those self-adjoint extensions of a lower semi-bounded symmetric operator on Hilbert space which have the same lower bound as the Friedrichs extension. Applications of this…

In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves…

The self adjoint operator of time in non-relativistic quantum mechanics is found within the approach where the ordinary Hamiltonian is not taken to be conjugate to time. The operator version of the reexpressed Liouville equation with the…

In this work, firstly in the Hilbert space of vector-functions L^2 (H,(-\infty,a)\bup(b,+\infty)),a<b all selfadjoint extensions of the minimal operator generated by linear singular symmetric differential expression l(\cdot)=i d/dt+A with a…

We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…