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Despite the fact that it is not integrable, the 1 + 2-dimensional Sine-Gordon equation has N-soliton solutions, whose velocities are lower than the speed of light (c = 1), for all N greater than or equal to 1. Based on these solutions, a…
A generalized harmonic oscillator on noncommutative spaces is considered. Dynamical symmetries and physical equivalence of noncommutative systems with the same energy spectrum are investigated and discussed. General solutions of…
The one-dimensional quantum harmonic oscillator problem is examined via the Laplace transform method. The stationary states are determined by requiring definite parity and good behaviour of the eigenfunction at the origin and at infinity.
The noncommutative harmonic oscillator in arbitrary dimension is examined. It is shown that the $\star$-genvalue problem can be decomposed into separate harmonic oscillator equations for each dimension. The noncommutative plane is…
Linear oscillators contribute to most branches of contemporary quantum science. They have already successfully served as quantum sensors and memories, found applications in quantum communication, and hold promise for cluster-state-based…
We describe a new class of exact square integrable solutions of the Pauli and Dirac equation in rotating electromagnetic fields. Solutions obtained by putting equations in the stationary form with help of a coordinate transformation…
Complete description of the classical and quantum dynamics of a particle in an anisotropic, rotating, harmonic trap is given. The problem is studied in three dimensions and no restrictions on the geometry are imposed. In the generic case,…
Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with…
We study the possible generalized boundary conditions and the corresponding solutions for the quantum mechanical oscillator model on K\"{a}hler conifold. We perform it by self-adjoint extension of the the initial domain of the effective…
Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…
We have obtained the solutions of two dimensional singular oscillator which is known as the quantum Calogero-Sutherland model both in cartesian and parabolic coordinates within the framework of quantum Hamilton Jacobi formalism. Solvability…
An explicit solution of the equation for the classical harmonic oscillator with smooth switching of the frequency has been found . A detailed analysis of a quantum harmonic oscillator with such frequency has been done on the base of the…
The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat…
This paper is devoted to find the exact solution of the harmonic oscillator in a position-dependent 4-dimensional noncommutative phase space. The noncommutative phase space that we consider is described by the commutation relations between…
An exactly-solvable model of the non-relativistic harmonic oscillator with a position-dependent effective mass is constructed. The model behaves itself as a semi-infinite quantum well of the non-rectangular profile. Such a form of the…
The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.
The independent eigenstates of the total orbital angular momentum operators for a three-body system in an arbitrary D-dimensional space are presented by the method of group theory. The Schr\"{o}dinger equation is reduced to the generalized…
The finite q-oscillator is a model that obeys the dynamics of the harmonic oscillator, with the operators of position, momentum and Hamiltonian being functions of elements of the q-algebra su_q(2). The spectrum of position in this discrete…
We propose the simple quantum model of nonlinear autonomous oscillator in hard excitation regime. We originate from classical equations of motion for similar oscillator and quantize them using the Lindblad master equation for the density…
We present an exact solution of a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent on the position. The free Hamiltonian of the proposed model has the form…