2,596 research outputs found
Bound State Wave Functions through the Quantum Hamilton - Jacobi Formalism
The bound state wave functions for a wide class of exactly solvable
potentials are found utilizing the quantum Hamilton-Jacobi formalism. It is
shown that, exploiting the singularity structure of the quantum momentum
function, until now used only for obtaining the bound state energies, one can
straightforwardly find both the eigenvalues and the corresponding
eigenfunctions. After demonstrating the working of this approach through a
number of solvable examples, we consider Hamiltonians, which exhibit broken and
unbroken phases of supersymmetry. The natural emergence of the eigenspectra and
the wave functions, in both the unbroken and the algebraically non-trivial
broken phase, demonstrates the utility of this formalism.Comment: replaced with the journal versio
Scattering Wave Functions at Bound State Poles
The normalisation relation between the bound and scattering S-state wave
functions, extrapolated to the bound state pole, is derived from the
Schroedinger equation. It is shown that, unlike previous work, the result does
not depend on the details of the potential through the corresponding Jost
function but is given uniquely in terms of the binding energy. The
generalisations to higher partial waves and one-dimensional scattering are
given.Comment: 15 pages Latex. No graph
Sufficiency Criterion for the Validity of the Adiabatic Approximation
We examine the quantitative condition which has been widely used as a
criterion for the adiabatic approximation but was recently found insufficient.
Our results indicate that the usual quantitative condition is sufficient for a
special class of quantum mechanical systems. For general systems, it may not be
sufficient, but it along with additional conditions is sufficient. The usual
quantitative condition and the additional conditions constitute a general
criterion for the validity of the adiabatic approximation, which is applicable
to all dimensional quantum systems. Moreover, we illustrate the use of the
general quantitative criterion in some physical models.Comment: 9 pages, no figure,appearing in PRL98(2007)15040
Quantum mechanical Carnot engine
A cyclic thermodynamic heat engine runs most efficiently if it is reversible.
Carnot constructed such a reversible heat engine by combining adiabatic and
isothermal processes for a system containing an ideal gas. Here, we present an
example of a cyclic engine based on a single quantum-mechanical particle
confined to a potential well. The efficiency of this engine is shown to equal
the Carnot efficiency because quantum dynamics is reversible. The quantum heat
engine has a cycle consisting of adiabatic and isothermal quantum processes
that are close analogues of the corresponding classical processes.Comment: 10 page
Equivalence Theorems for Pseudoscalar Coupling
By a unitary transformation a rigorous equivalence theorem is established for the pseudoscalar coupling of pseudoscalar mesons (neutral and charged) to a second-quantized nucleon field. By the transformation the linear pseudoscalar coupling is eliminated in favor of a nonlinear pseudovector coupling term together with other terms. Among these is a term corresponding to a variation of the effective rest mass of the nucleons with position through its dependence on the meson potentials. The question of the connection of the nonlinear pseudovector coupling with heuristic proposals that such a coupling may account for the saturation of nuclear forces and the independence of single nucleon motions in nuclei is briefly discussed. The new representation of the Hamiltonian may have particular value in constructing a strong coupling theory of pseudoscalar coupled meson fields. Some theorems on a class of unitary transformations of which the present transformation is an example are stated and proved in an appendix.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86126/1/PhysRev.87.1061-RKO.pd
Perturbative and non-perturbative studies with the delta function potential
We show that the delta function potential can be exploited along with
perturbation theory to yield the result of certain infinite series. The idea is
that any exactly soluble potential if coupled with a delta function potential
remains exactly soluble. We use the strength of the delta function as an
expansion parameter and express the second-order energy shift as an infinite
sum in perturbation theory. The analytical solution is used to determine the
second-order energy shift and hence the sum of an infinite series. By an
appropriate choice of the unperturbed system, we can show the importance of the
continuum in the energy shift of bound states.Comment: 19 pages, 2 table
Critical view of WKB decay widths
A detailed comparison of the expressions for the decay widths obtained within
the semiclassical WKB approximation using different approaches to the tunneling
problem is performed. The differences between the available improved formulae
for tunneling near the top and the bottom of the barrier are investigated.
Though the simple WKB method gives the right order of magnitude of the decay
widths, a small number of parameters are often fitted. The need to perform the
fitting procedure remaining consistently within the WKB framework is emphasized
in the context of the fission model based calculations. Calculations for the
decay widths of some recently found super heavy nuclei using microscopic
alpha-nucleus potentials are presented to demonstrate the importance of a
consistent WKB calculation. The half-lives are found to be sensitive to the
density dependence of the nucleon-nucleon interaction and the implementation of
the Bohr-Sommerfeld quantization condition inherent in the WKB approach.Comment: 18 pages, Late
Graduate Quantum Mechanics Reform
We address four main areas in which graduate quantum mechanics education can
be improved: course content, textbook, teaching methods, and assessment tools.
We report on a three year longitudinal study at the Colorado School of Mines
using innovations in all these areas. In particular, we have modified the
content of the course to reflect progress in the field in the last 50 years,
used textbooks that include such content, incorporated a variety of teaching
techniques based on physics education research, and used a variety of
assessment tools to study the effectiveness of these reforms. We present a new
assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further
testing of a previously developed assessment tool, the Quantum Mechanics
Conceptual Survey. We find that graduate students respond well to
research-based techniques that have been tested mainly in introductory courses,
and that they learn much of the new content introduced in each version of the
course. We also find that students' ability to answer conceptual questions
about graduate quantum mechanics is highly correlated with their ability to
solve calculational problems on the same topics. In contrast, we find that
students' understanding of basic undergraduate quantum mechanics concepts at
the modern physics level is not improved by instruction at the graduate level.Comment: accepted to American Journal of Physic
Photodissociation of p-process nuclei studied by bremsstrahlung induced activation
A research program has been started to study experimentally the
near-threshold photodissociation of nuclides in the chain of cosmic heavy
element production with bremsstrahlung from the ELBE accelerator. An important
prerequisite for such studies is good knowledge of the bremsstrahlung
distribution which was determined by measuring the photodissociation of the
deuteron and by comparison with model calculations. First data were obtained
for the astrophysically important target nucleus 92-Mo by observing the
radioactive decay of the nuclides produced by bremsstrahlung irradiation at
end-point energies between 11.8 MeV and 14.0 MeV. The results are compared to
recent statistical model calculations.Comment: 6 pages, 8 figures, Proceedings Nuclear Physics in Astrophysics II,
May 16-20, 2005, Debrecen, Hungary. The original publication is available at
www.eurphysj.or
Three manifestations of the pulsed harmonic potential
We consider, in turn, three systems being acted upon by a regularly pulsed
harmonic potential (PHP). These are i) a classical particle, ii) a quantum
particle, and iii) a directed line. We contrast the mechanics of the first two
systems by parameterizing their bands of stability and periodicity. Interesting
differences due to quantum fluctuations are examined in detail. The
fluctuations of the directed line are calculated in the two cases of a binding
PHP, and an unbinding PHP. In the latter case there is a finite maximum line
length for a given potential strength.Comment: 34 Revtex pages, with 5 attached figure
- …