Related papers: Quantum mechanics on the noncommutative plane and …
We find the covariant deformed Heisenberg algebra and the Laplace-Beltrami operator on the extended $h$-deformed quantum plane and solve the Schr\"odinger equations explicitly for some physical systems on the quantum plane. In the…
We point out the connection between the problem of formulating quantum mechanics in phase space and projecting the motion of a quantum mechanical particle onto a particular Landau level. In particular, we show that lowest Landau level wave…
The problem of diamagnetism, solved by Landau, continues to pose fascinating issues which have relevance even today. These issues relate to inherent quantum nature of the problem, the role of boundary and dissipation, the meaning of…
The central theme of this thesis is to study some aspects of noncommutative quantum mechanics and noncommutative quantum field theory. We explore how noncommutative structures can emerge and study the consequences of such structures in…
Effects of noncommutativity are investigated in planar quantum mechanics in the coordinate representation. Generally these issues are addressed by converting to the momentum space. In the first part of the work we show noncommutative…
We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wavefunctions of the system.…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
An electron moving on plane in a uniform magnetic field orthogonal to plane is known as the Landau problem. Wigner functions for the Landau problem when the plane is noncommutative are found employing solutions of the Schroedinger equation…
We consider the dynamics of a charged particle interacting with background electromagnetic field under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. Following the prescription in…
The supersymmetric quantum mechanics of a two-dimensional non-relativistic particle subject to external magnetic and electric fields is studied in a superfield formulation and with the typical non-minimal coupling of (2+1) dimensions. Both…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
Motivated by string theory an extension of the Landau problem to quantum field theory is considered. We show that the commutator between momenta of the fields violates Lorentz and CPT invariance leading to an alternative method of…
The quantum dynamics of a two-dimensional charged spin $1/2$ particle is studied for general, symmetry--free curved surfaces and general, nonuniform magnetic fields that are, when different from zero, orthogonal to the defining two surface.…
The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a…
Physics of two-dimensional electron gases under perpendicular magnetic field often displays three distinct stages when increasing the field amplitude: a low field regime with classical magnetotransport, followed at intermediate field by a…
The free scalar field is studied on the Y-junction of three semi infinite axes which is the simplest example of a non-manifold space. It is shown that under an assumption that the junction point can not gain a macroscopic amount of energy…
We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of…
I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…