相关论文: Quantum Mechanics with Difference Operators
Quantum kernel methods (QKMs) have emerged as a prominent framework for supervised quantum machine learning. Unlike variational quantum algorithms, which rely on gradient-based optimisation and may suffer from issues such as barren…
In this paper we develope the main ideas of the quantized version of affinely-rigid (homogeneously deformable) motion. We base our consideration on the usual Schr\"odinger formulation of quantum mechanics in the configuration manifold which…
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum…
Difference Kinetic Equations are derived quantum mechanically in a plane wavelets representation with account of two-particle correlations. It is shown that the set of plane wavelet orthonormal functions is complete. The set of ket vectors…
Starting with the first-order singular Lagrangian, the canonical structures of the noncommutative quantum system on a submanifold embedded in the higher-dimensional Euclidean space are investigated with the projection operator method (POM)…
Quantization together with quantum dynamics can be simultaneously formulated as the problem of finding an appropriate flat connection on a Hilbert bundle over a contact manifold. Contact geometry treats time, generalized positions and…
The algebra of quantum differential operators on graded algebras was introduced by V. Lunts and A. Rosenberg. D. Jordan, T. McCune and the second author have identified this algebra of quantum differential operators on the polynomial…
A general formulation of noncommutative or quantum derivatives for operators in a Banach space is given on the basis of the Leibniz rule, irrespective of their explicit representations such as the G\^ateaux derivative or commutators. This…
Following the definition of quantum differential operators given by Lunts and Rosenberg in (Sel. math., New ser. 3 (1997) 335--359), we show that the ring of quantum differential operators on the affine line is the ring generated by x and…
The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.
Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. The algebra of these operators is analyzed in detail; it is…
The basic principles of the quantum mechanics in the K-field formalism are stated in the paper. The basic distinction of this theory arises from that the quantum theory equations (including well-known Schrodinger, Klein-Gordon and quadratic…
The Verma modules over the quantum groups $\mathrm U_q(\mathfrak{gl}_{l + 1})$ for arbitrary values of $l$ are analysed. The explicit expressions for the action of the generators on the elements of the natural basis are obtained. The…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
Quantum--mechanical operators corresponding to canonical momentum and position of a point--like particle, which follow from the quantum field theory in the general Riemannian space-time, satisfy generally to a deformation of the canonical…
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…
This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…
In a series of papers we have argued that the 'basic' physical procedure of minimal coupling giving the quantum description of a Hamiltonian system interacting with a magnetic field, can be given a very satisfactory mathematical formulation…
Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…