Related papers: Energy partition for anharmonic, undamped, classic…
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 propose an efficient method to compute the vacuum polarization energy of static field configurations that do not allow a decomposition into symmetric and anti-symmetric channels in one space dimension. In particular we compute the vacuum…
We describe a method for the calculation of accurate energy eigenvalues and expectation values of observables of separable quantum-mechanical models. We discuss the application of the approach to one-dimensional anharmonic oscillators with…
The applicability of the factorization method is extended to the case of quantum fractional-differential Hamiltonians. In contrast with the conventional factorization, it is shown that the `factorization energy' is now a…
We derive the gravitational and electrostatic self-energies of a particle at rest in the background of a cosmic dispiration (topological defect), finding that the particle may experience potential steps, well potentials or potential…
Two equations are constructed which reflect, for fermions moving independently in a spherical harmonic potential, a differential virial theorem and a relation between the turning points of kinetic energy and particle densities. These…
The energy of extended classical objects, such as vortices, depends on their shape. In particular, we show that the curvature energy of a kink in two spatial dimensions, as a prototype of extended classical solutions, is always negative. We…
In this article, the optimal control problem for a harmonic oscillator with an inequality constraint is considered. The applied energy of the oscillator during a fixed final time period is used as the performance criterion. The analytical…
In the statistical mechanics of quantum harmonic oscillators, the zero-point energy can either be included (Schr\"odinger oscillators) or omitted (Planck oscillators). For the usual results, the type of oscillator makes no difference but,…
In this note, we use an elementary argument to show that the existence and unitarity of radiation fields implies asymptotic partition of energy for the corresponding wave equation. This argument establishes the equipartition of energy for…
One dimensional quantum mechanics problems, namely the infinite potential well, the harmonic oscillator, the free particle, the Dirac delta potential, the finite well and the finite barrier are generalized for finite arbitrary dimension in…
From the energy-momentum tensors of the electromagnetic field and the mechanical energy-momentum, the equations of energy conservation and balance of electromagnetic and mechanical forces are obtained. The equation for the Abraham force in…
A method for determination of bound state energies for an asymmetric quantum well with an arbitrary shape of the bottom is suggested. It is shown that how the equation determining the energy levels can be easily derived if one knows the…
Many-body quantum-mechanical stationary states that have real valued wavefunctions are shown to satisfy a classical conservation of energy equation with a kinetic energy function. The terms in the equation depend on the probability…
Inhomogeneous plasmas and fluids contain energy stored in inhomogeneity and they naturally tend to relax into lower energy states by developing instabilities or by diffusion. But the actual amount of energy in such inhomogeneities has…
We perform a study of various anharmonic potentials using a recently developed method. We calculate both the wave functions and the energy eigenvalues for the ground and first excited states of the quartic, sextic and octic potentials with…
This paper focuses on the escape problem of a harmonically-forced classical particle from a purely-quartic truncated potential well. The latter corresponds to various engineering systems that involve purely cubic restoring force and absence…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
The energy conservation is a general law of nature. In the classical physics, the energy W_{AB} of a conservative system {AB} that contains the objects A and B is equal to a sum of the positive energies W_A and W_B of the isolated objects A…
The Orthodox kinetic energy has, in fact, two hidden-variable components: one linked to the current (or Bohmian) velocity, and another linked to the osmotic velocity (or quantum potential), and which are respectively identified with phase…