Related papers: Step Momentum Operator
Quantum physics is generally concerned with real eigenvalues due to the unitarity of time evolution. With the introduction of $\mathcal{PT}$ symmetry, a widely accepted consensus is that, even if the Hamiltonian of the system is not…
Eigenfunctions and eigenvalues of the operator of the square of the angular momentum are studied. It is shown that neither from the requirement for the eigenfunctions be normalizable nor from the commutation relations it is possible to…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
The definition of the standard differential operator is extended from integer steps to arbitrary stepsize. The classical, nonrelativistic Hamiltonian is quantized, using these new continuous operators. The resulting Schroedinger type…
It is the purpose of the present contribution to demonstrate that the generalization of the concept of a quantum mechanical observable from the Hermitian operator of standard quantum mechanics to a positive operator-valued measure is not a…
The Hermitian Cartesian quantum momentum operator $\mathbf{p}$ for an embedded surface $M$ in $R^{3}$ is proved to be a constant factor $-i\hbar $ times the mean curvature vector field $H\mathbf{n}$ added to the usual differential term.…
The quantization of a single particle without spin in an appropriate curved space-time is considered. The Hamilton formalism on reduced space for a particle in a curved space-time is constructed and the main aspects of quantization scheme…
In two recent papers exact Hermite-Gaussian solutions to relativistic wave equations have been obtained for both electromagnetic and particle beams that include Gouy phase. The solutions for particle beams correspond to those of the…
We consider the quantum problem of a particle in either a spherical box or a finite spherical well confined by a circular cone with an apex angle $2\theta_0$ emanating from the center of the sphere, with $0<\theta_0<\pi$. This non-central…
We study the problem of computing the probability for the time-of-arrival of a quantum particle at a given spatial position. We consider a solution to this problem based on the spectral decomposition of the particle's (Heisenberg) state…
We study the physics of quantum phase transitions from the perspective of non-equilibrium thermodynamics. For first order quantum phase transitions, we find that the average work done per quench in crossing the critical point is…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…
The extraordinary success in laser cooling, trapping, and coherent manipulation of atoms has energized the efforts in extending this exquisite control to molecules. Not only are molecules ubiquitous in nature, but the control of their…
The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take…
The eigenvalue equations for the energy of bound states of a particle in a square well are solved, and the exact solutions are obtained, as power series. Accurate analytical approximate solutions are also given. The application of these…
We study the bound-state solutions of vanishing angular momentum in a quaternionic spherical square-well potential of finite depth. As in the standard quantum mechanics, such solutions occur for discrete values of energies. At first glance,…
The thermodynamic limit of the internal energy and the entropy of the system of quantum interacting particles in random medium is shown to exist under the crucial requirements of stability and temperedness of interactions. The energy turns…
We discuss the requirement of single valuedness and periodicity of eigenfunction of the third component of the operator of angular momentum. This condition, imposed on a non observable, is often used to derive that the eigenvalues of…
The momentum representation is seldom used in quantum mechanics courses. Some students are thence surprised by the change in viewpoint when, in doing advanced work, they have to use the momentum rather than the coordinate representation. In…
The Newtonian concept of force may be useful in some aspects of the dynamics of many-particle quantum systems such as fissioning nuclei. Following Ehrenfest's method, we show that the quantum kinetic force between parts of an extended…