相关论文: Non-hermitian techniques of canonical transformati…

Canonical transformations using the idea of quantum generating functions are applied to construct a quantum Hamilton-Jacobi theory, based on the analogy with the classical case. An operator and a c-number forms of the time-dependent quantum…

Quantum canonical transformations of the second kind and the non-Hermitian realizations of the basic canonical commutation relations are investigated with a special interest in the generalization of the conventional ladder operators. The…

The non-Hermitian Schr\"odinger equation is re-expressed generally in the form of Hamilton's canonical equation without any approximation. Its quantization called non-Hermitian quantum field theory is discussed. By virtue of the canonical…

We investigate two methods of constructing a solution of the Schr\"{o}dinger equation from the canonical transformation in classical mechanics. One method shows that we can formulate the solution of the Schr\"{o}dinger equation from linear…

By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…

We generalize a recently proposed algebraic method in order to treat non-Hermitian Hamiltonians. The approach is applied to several quadratic Hamiltonians studied earlier by other authors. Instead of solving the Schr\"odinger equation we…

In this work we intend to study a class of time-dependent quantum systems with non-Hermitian Hamiltonians, particularly those whose Hermitian counterpart are important for the comprehension of posed problems in quantum optics and quantum…

In this work we show how to complete some Hamilton-Jacobi solutions of linear, nonconservative classical oscillatory systems which appeared in the literature and we extend these complete solutions to the quantum mechanical case. In…

A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…

In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians…

The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the…

The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…

We show that the Markovian dynamics of two coupled harmonic oscillators may be analyzed using a Schr\"odinger equation and an effective non-Hermitian Hamiltonian. This may be achieved by a non-unitary transformation that involves…

Quantum canonical transformations have attracted interest since the beginning of quantum theory. Based on their classical analogues, one would expect them to provide a powerful quantum tool. However, the difficulty of solving a nonlinear…

This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…

The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized…

In this paper a quantum mechanics is built by means of a non-Hermitian momentum operator. We have shown that it is possible to construct two Hermitian and two non-Hermitian type of Hamiltonians using this momentum operator. We can construct…

We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectrum, and transit to the Hermitian…

We use the Fourier operator to transform a time dependent mass quantum harmonic oscillator into a frequency dependent one. Then we use Lewis-Ermakov invariants to solve the Schr\"odinger equation by using squeeze operators. Finally we give…

Harmonic oscillator in noncommutative two dimensional lattice are investigated. Using the properties of non-differential calculus and its applications to quantum mechanics, we provide the eigenvalues and eigenfunctions of the corresponding…