Showing papers on "Finite potential well published in 1985"

Improving on the conventional presentation of molecular vibrations: Advantages of the pseudoharmonic potential and the direct construction of potential energy curves

Abstract: Two improvements in the discussion of molecular vibrations are suggested. First, the pseudoharmonic potential possesses advantages over the harmonic: as a proper potential should, it has a larger force constant inside the equilibrium distance than outside and becomes infinite for zero distance. Its eigenvalues and eigenfunctions may be obtained in closed form either by the power series method or by manipulation of the Schrodinger equation into a standard form. Unlike the harmonic case, this is still true in the presence of a centrifugal potential. The second improvement involves a direct method of constructing a potential energy curve from the energy levels, rather than adjusting parameters in a potential so that calculated energy levels fit experimental values. The method, which involves the instructive semiclassical momentum, is illustrated for the harmonic and pseudoharmonic potentials, with an apparent paradox cleared up.

An exact result for the incoherent scattering function in dilute suspensions

Abstract: The effect of a square well potential added to the hard core repulsion, between particles in a dilute suspension, on their self‐diffusion coefficient is investigated on the basis of the results, obtained by Batchelor, for the mobility of these particles. Hydrodynamic interactions are neglected. It is found that a moderately strong attractive potential leads to an increase of the self‐diffusion coefficient, whereas a repulsive potential has the opposite effect. The exact result for the incoherent scattering function is given. The results for the self‐diffusion coefficient are recovered in the long time limit. The short time behavior is also discussed and some conclusions are drawn.

Improved simple graphical solution for the eigenvalues of the finite square well potential

Abstract: The three principal graphical methods for obtaining the energy eigenvalues of the finite square well potential are presented The simplest method, with sine, cosine and straight line, is provided with an easily applied rule, based on a physically obvious argument, for eliminating the unacceptable roots The forms of the wavefunctions within the well, and the corresponding linear probability densities, are derived directly from the method A simple extension of the method allows the energy level spectrum to be obtained directly on a linear energy scale The variations of the energy eigenvalues with well depth and width are separately and jointly displayed, and explicit corresponding functional relationships are derived Finally, two universal graphs are deduced, each of which allows the rapid appreciation and calculation of the dependence of the energy levels on the depth and width of the well and on the mass of the particle

Experimental studies of potential problems in quantum mechanics using nonlinear transmission line

Abstract: The experimental method for solving the potential problem in quantum mechanics is demonstrated using the nonlinear transmission line equivalent to the Korteweg–de Vries equation (K–dV equation) Ut−6UUx+Uxxx=0. An input voltage pulse corresponding to the potential is observed to dissolve into a finite train of solitons propagating along the line. The signal voltage consisting of solitons is compared with the solution of the initial‐value problem for the K–dV equation, which is exactly solved by the theory called the ‘‘inverse scattering method.’’ Consequently, it is shown that the number of bound states and discrete energy levels for one‐dimensional potentials (square well potential, −U0 sech2 αx potential, and the Kronig–Penny potential) are determined by observing the signal waveform without calculations.

On a Probabilistic Model of Infinite Quantum Mechanical Particle Systems

Abstract: The usual formulation of quantum mechanics with help of the SCHRODINGER equation is possible only for systems with a finite number of particles. In the present paper we propose a new formulation in terms of random point processes which is applicable without any mathematical changes both for finite and for infinite particle systems. Up to now it is restricted to a non-relativistic description of pure states of boson systems. For finite particle systems this approach is equivalent to the usual HILBERT space formulation of quantum mechanics. Especially we consider POISSON states representing systems of (possibly infinite) independent bosons. Further, we give sufficient conditions for invariance (i.e., for stationary states) and we discuss invariance in the case of a system of coupled harmonic oscillators.

Probability current conservation imposed on nucleon knockout amplitudes.

Abstract: We construct nucleon knockout amplitudes which exactly satisfy probability current conservation. The derivation is first produced for a nucleon bound to an inert core and is then generalized to the case of realistic nuclei. Numerical tests are presented for a nucleon bound in a square well potential for which exact results are compared with several approximated ones; the need of imposing probability current conservation is also numerically demonstrated.