Related papers: The ubiquitous XP commutator
Position and momentum observables are considered and their correlation is studied for the simplest quantum system of a free particle moving in one dimension. The algebra and the eigenvalue problem for the correlation observable is presented…
A system of a particle and a harmonic oscillator, which have pure point spectrum if uncoupled, is known to acquire absolutely continuous spectrum when the particle and the oscillator are coupled by a sufficiently strong point interaction.…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
The notion of incompressible momentum observables is introduced. It is shown that when the metric in a manifold has a certain form, a set of canonically conjugate variables Xk and Pk in which Pk are incompressible, can be constructed. Based…
It is shown that the Fourier transformation that relates position and momentum representations of quantum mechanics can be understood as a consequence of a symmetry principle that establishes the equivalence of being and becoming in the…
We study a general class of models whose classical Hamiltonians are given by H = U(x) p + V(x)/p, where x and p are the position and momentum of a particle moving in one dimension, and U and V are positive functions. This class includes the…
Two generalizations of Kempf's quadratic canonical commutation relation in one dimension are considered. The first one is the most general quadratic commutation relation. The corresponding nonzero minimal uncertainties in position and…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
If space is indistinguishable from the extension of a physical body, as is Descartes's conception, then transformations of space become transformations of physical bodies. Every point of space then has properties of physical bodies in some…
Moments are expectation values of products of powers of position and momentum, taken over quantum states (or averages over a set of classical particles). For free particles, the evolution in the quantum case is closely related to that of a…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
It seems that the problem of finding a suitable position operator for photon has been solved in a recently published work which is based on a new commutation relation between position and momentum operators of massless particles[1].…
We investigate the problem of coexistence of position and momentum observables. We characterize those pairs of position and momentum observables which have a joint observable.
We consider the quantum dynamics of a single particle in the plane under the influence of a constant perpendicular magnetic and a crossed electric potential field. For a class of smooth and small potentials we construct a non-trivial…
A (M4 x M4) x Z4 model, describing an extended particle composed of two local modes and represented by a field psi(x, xi ;z), is formulated in its most general form (x, xi ; z) belong to (M4 x M4) x Z4. The 'z' argument specifies whether…
It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that…
The deduction of a constant of motion, a Lagrangian, and a Hamiltonian for relativistic particle moving in a dissipative medium characterized by a force which depends on the square of the velocity of the particle is done. It is shown that…
An essential prerequisite for the study of q-deformed physics are particle states in position and momentum representation. In order to relate x- and p-space by Fourier transformations the appropriate q-exponential series related to…
Under the assumption that every material object can ultimately be described by quantum theory, we ask how a probe system evolves in a device prepared and kept in a superposition state of values of its classical parameter. We find that,…
Inspired by an old idea of von Neumann, we seek a pair of commuting operators X,P which are, in a specific sense, "close" to the canonical non-commuting position and momentum operators, x,p. The construction of such operators is related to…