Related papers: Quantum effective force in an expanding infinite s…
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…
By expressing the Schr\"odinger wave function in the form $\psi=Re^{iS/\hbar}$, where $R$ and $S$ are real functions, we have shown that the expectation value of $S$ is conserved. The amplitude of the wave ($R$) is found to satisfy the…
Using classical statistics, Schrodinger equation in quantum mechanics is derived from complex space model. Phase-space probability amplitude, that can be defined on classical point of view, has connections to probability amplitude in…
We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We first prove that contrary to earlier claims, there is no strong nonlocality: a quantum state localized at the…
Exact solutions of time-dependent Schr\"odinger equation in presence of time-dependent potential is defined by point transformation and separation of variables. Energy and Heisenberg uncertainty relation are pursued for time-independent…
When numerically simulating the unitary time evolution of an infinite-dimensional quantum system, one is usually led to treat the Hamiltonian $H$ as an "infinite-dimensional matrix" by expressing it in some orthonormal basis of the Hilbert…
The momentum operator for a spin-less particle when confined to a 2D surface embedded into 3D space acquires a geometrical component proportional to the mean curvature that renders it Hermitian. As a consequence, the quantum force operator…
The finite square potential well is a staple problem in introductory quantum mechanics. There is an extensive literature on the determination of the allowed energies, which requires the solution of a transcendental equation by numerical,…
We propose a model of dynamical noncommutative quantum mechanics in which the noncommutative strengths, describing the properties of the commutation relations of the coordinate and momenta, respectively, are arbitrary energy dependent…
An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…
We describe the dynamics of a bound state of an attractive $\delta$-well under displacement of the potential. Exact analytical results are presented for the suddenly moved potential. Since this is a quantum system, only a fraction of the…
I develop the solution to the problem of an electron confined in a composite quadratic well subject to a simple, external periodic force. The method of solution illustrates several of the basic techniques useful in formally solving the…
We develop the formalism of quantum mechanics on three dimensional fuzzy space and solve the Schr\"odinger equation for a free particle, finite and infinite fuzzy wells. We show that all results reduce to the appropriate commutative limits.…
We present a solution of the quantum mechanics problem of the allowable energy levels of a bound particle in a one-dimensional finite square well. The method is a geometric-analytic technique utilizing the conformal mapping $w \to z = w…
The particle in a well in dimension one is a classical problem in quantum mechanics. We study higher-dimensional analogues of the problem, where the well is a smooth domain in $\mathbb{R}^d$. We show that simple eigenvalues and…
Aspects of quantum mechanics on a ring are studied. Either one or two impenetrable barriers are inserted at nodal and non-nodal points to turn the ring into either one or two infinite square wells. In the process, the wave function of a…
Using a recent reformulation of quantum mechanics where the potential function is not required, we are able to obtain the energy spectrum and wave function associated with the infinite square well analytically. Therefore, this work…
The evolution problem for a quantum particle confined in a 1D box and interacting with one fixed point through a time dependent point interaction is considered. Under suitable assumptions of regularity for the time profile of the…
We take a closer and new look at the effects of tidal forces on the free fall of a quantum particle inside a spherically symmetric gravitational field. We derive the corresponding Schr\"odinger equation for the particle by starting from the…
We study the temporal formation of quantum mechanical bound states within a one-dimensional attractive square-well potential, by first solving the time-independent Schroedinger equation and then study a time dependent system with an…