Related papers: Critical comments on the quantization of the angul…
In the present study, the concept of a quantum particle with step momentum is introduced. The energy eigenvalues and eigenfunctions of such particles are obtained in the context of the generalized momentum operator, proposed recently in…
We study perturbations of the self-adjoint periodic Sturm--Liouville operator \[ A_0 = \frac{1}{r_0}\left(-\frac{\mathrm d}{\mathrm dx} p_0 \frac{\mathrm d}{\mathrm dx} + q_0\right) \] and conclude under $L^1$-assumptions on the differences…
The quantum mechanical expression relating two commuting operators is reformulated such that the power method (also called method of moments) for iteratively calculating eigenvalues and eigenvectors becomes applicable. The new iterative…
We tried to determine the range of validity of a recently proposed modification of the Hellmann potential that leads to analytical eigenvalues and eigenfunctions. We discuss the difficulties that we found in the analysis of the main…
The applicability of the factorization method is extended to the case of quantum fractional-differential Hamiltonians. In contrast with the conventional factorization, it is shown that the `factorization energy' is now a…
Using three different notions of generalized principal eigenvalue of linear second order elliptic operators in unbounded domains, we derive necessary and sufficient conditions for the validity of the maximum principle, as well as for the…
The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an…
We give analytical expressions for the eigenvalues and generalized eigenfunctions of $\hat{T}_3$, the $z$-axis projection of the toroidal dipole operator, in a system consisting of a particle confined in a thin film bent into a torus shape.…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
We perform analytical and quantitative analysis of the motion of a non-integrable pendulum with two degrees of freedom, in which an integrable nonlinear pendulum and a harmonic oscillator are weakly coupled through a non-integrable…
Consider a positive operator $T$ on an $L^p$-space (or, more generally, a Banach lattice) which increases the support of functions in the sense that $supp(Tf) \supseteq supp{f}$ for every function $f \ge 0$. We show that this implies, under…
It is known that, if a locally perturbed periodic self-adjoint operator on a combinatorial or quantum graph admits an eigenvalue embedded in the continuous spectrum, then the associated eigenfunction is compactly supported--that is, if the…
We study the eigenvalue problem for the complex Monge-Amp\`ere operator in bounded hyperconvex domains in $\C^n$, where the right-hand side is a non-pluripolar positive Borel measure. We establish the uniqueness of eigenfunctions in the…
The paper is devoted to the study of some properties of the first eigenvalue of the anisotropic $p$-Laplace operator with Robin boundary condition involving a function $\beta$ which in general is not constant. In particular we obtain sharp…
The so-called eigenvalue-eigenstate link states that no property can be associated to a quantum system unless it is in an eigenstate of the corresponding operator. This precludes the assignation of properties to unmeasured quantum systems…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
A universal energy eigenvalue equation is proposed in this paper. It is proven that the unique set of eigenfunctions or preferred basis exists for any non-isolated sub-system. Applying the new eigenvalue equation to the relative motion of a…
Eigenfunctions of total angular momentum for a charged vector field interacting with a magnetic monopole are constructed and their properties studied. In general, these eigenfunctions can be obtained by applying vector operators to the…
We argue that quantum mechanics makes sense without such controversial postulates as the wave function collapse, the quantum probability rule and the observable postulate. We only need the existence of a wave function as a representation of…
The quantum theory of rotation angles (S. M. Barnett and D. T. Pegg, Phys. Rev. A, 41, 3427-3425 (1990)) is generalised to non-integer values of the orbital angular momentum. This requires the introduction of an additional parameter, the…