Related papers: Equivalence between free quantum particles and tho…
A set of zero-range scatterers along its axis lifts the integrability of a harmonic waveguide. Effective solution of the Schr\"odinger equation for this model is possible due to the separable nature of the scatterers and millions of…
The general and explicit relation between the phase time and the dwell time for quantum tunneling or scattering is investigated. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, here we…
We obtain the geometric phase for states of a particle in a spherical infinite potential well with a moving wall in two different cases; First, when the radius of the well increases (or decreases) monotonically. Second, when the radius…
We propose a general framework to study transformations that drive an underdamped Brownian particle in contact with a thermal bath from an equilibrium state to a new one in an arbitrarily short time. To this end, we make use of a time and…
The solution of the time-dependent Schr\"odinger equation is discussed for a particle confined in half-space $x>0$ with a linear potential $V(x)=Kx$ in the following situations: (a) sudden removal of the wall and switching on the linear…
We develop a classical picture of interference for non-interacting individual classical massive free particles. As long as they remain undetected, particles carry the information of a phase equal to an action integral along their…
A matrix inverse free method to solve time-dependent Schrodinger equation is presented. The method is not subject to form of Hamiltonian and adopting real space grid system such as structured and unstructured grid, and achieves the order N…
In quantum mechanics, a classical particle is raised to a wave-function, thereby acquiring many more degrees of freedom. For instance, in the semi-classical regime, while the position and momentum expectation values follow the classical…
New families of time-dependent potentials related to the parametric oscillator are introduced. This is achieved by introducing some general time-dependent operators that factorize the appropriate constant of motion (quantum invariant) of…
In this paper, we investigate the quantum entanglement induced by phase-space noncommutativity. Both the position-position and momentum-momentum noncommutativity are incorporated to study the entanglement properties of coordinate and…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
The free expansion of a Gaussian wavepacket is a problem commonly discussed in undergraduate quantum classes by directly solving the time-dependent Schrodinger equation as a differential equation. In this work, we provide an alternative way…
Rotationally invariant space with noncommutativity of coordinates and noncommutativity of momenta of canonical type is considered. A system of $N$ interacting harmonic oscillators in uniform filed and a system of $N$ particles with harmonic…
Equilibrium phase transitions usually emerge from the microscopic behavior of many-body systems and are associated to interesting phenomena such as the generation of long-range order and spontaneous symmetry breaking. They can be defined…
The Snyder model is an example of noncommutative spacetime admitting a fundamental length scale $\beta$ and invariant under Lorentz transformations, that can be interpreted as a realization of the doubly special relativity axioms. Here, we…
The energy-based stochastic extension of the Schrodinger equation is perhaps the simplest mathematically rigourous and physically plausible model for the reduction of the wave function. In this article we apply a new simulation methodology…
The properties of a nonlinear oscillator with an additional term $k_g/x^2$, characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated…
Being comparable in quantum systems makes it possible for spaces with varying dimensions to attribute each other using special conversions can attribute schrodinger equation with like-hydrogen atom potential in defined dimensions to a…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…