相关论文: Canonical quantization on the half-line and in an …

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 paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…

Non commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non commutative configuration space. Taking this as departure point, we formulate a coherent state approach…

Although the Hamiltonian in quantum physics has to be a linear operator, it is possible to make quantum systems behave as if their Hamiltonians contained antilinear (i.e., semilinear or conjugate-linear) terms. For any given quantum system,…

Conventional canonical quantization procedures directly link various c-number and q-number quantities. Here, we advocate a different association of classical and quantum quantities that renders classical theory a natural subset of quantum…

We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…

Enhanced quantization offers a different classical/quantum connection than that of canonical quantization in which $\hbar >0$ throughout. This result arises when the only allowed Hilbert space vectors allowed in the quantum action…

At this paper, it is considered to find a way for defining non-commutative spaces by ordinary commutative ones and vice versa. A novel parameter which has not been considered so far is represented. This parameter describes equivalent…

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…

Different routes towards the canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for…

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…

Inspired by the recent work of Filho et al., a Hermitian momentum operator is introduced in a general curved space with diagonal metric. The modified Hamiltonian associated with this new momentum is calculated and discussed. Furthermore,…

The diagonalization of the metrical and canonical Hamilton operators of a scalar field with an arbitrary coupling, with a curvature in N-dimensional homogeneous isotropic space is considered in this paper. The energy spectrum of the…

This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…

We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…

While canonical quantization solves many problems there are some problems where it fails. A close examination of the classical/quantum connection leads to a new connection that permits quantum and classical realms to coexist, as is the case…

We study a pair of canonoid (fouled) Hamiltonians of the harmonic oscillator which provide, at the classical level, the same equation of motion as the conventional Hamiltonian. These Hamiltonians, say $K_{1}$ and $K_{2}$, result to be…

We perform the canonical analysis of the Holst action for general relativity with a cosmological constant without introducing second-class constraints. Our approach consists in identifying the dynamical and nondynamical parts of the…

Starting with the first-order singular Lagrangian, the canonical structure in the noncommutative quantum mechanics with the noncommutativities both of coordinates and momenta is investgated. Using the projection operator method (POM) for…

The three-dimensional quantum Euclidean space is an example of a non-commutative space that is obtained from Euclidean space by $q$-deformation. Simultaneously, angular momentum is deformed to $so_q(3)$, it acts on the $q$-Euclidean space…