WKB approximation

WKB Approximation of the Nonlinear Schr¨odinger-Newton Equations

Book 2.29 MB | Ebook Pages: 61
WKB Approximation of the Nonlinear Schr¨odinger-Newton Equations Carsten Hartmann† and Heinz-Ju¨rgen Schmidt‡ †Free University Berlin, Institute of Mathematics II
http://page.mi.fu-berlin.de/chartman/wkb.pdf



The Nonoscillatory Case

Book 5.63 MB | Ebook Pages: 78
WKB (Wentzel-Kramers-Brillouin) Approximation 1. We apply the WKB method to approximate solutions to equations of the form ε2y00 + q(x)y = 0, ε ˝ 1, (1)
http://www.math.unl.edu/~scohn1/8423/wkb.pdf

The WKB Approximation Lectures Nine and Ten The WKB Approximation pdf

The WKB Approximation Lectures Nine and Ten The WKB Approximation

Book 6.77 MB | Ebook Pages: 220
The WKB Approximation Lectures Nine and Ten The WKB Approximation The WKB method is a powerful tool to obtain solutions for many physIcal problems.
http://ocw.mit.edu/courses/mathematics/18-305-advanced-analytic-methods-in-science-and-engineering-fall-2004/lecture-notes/nineten.pdf

The WKB Approximation Lecture Eleven Turning Point pdf

The WKB Approximation Lecture Eleven Turning Point

Book 5.82 MB | Ebook Pages: 97
The WKB Approximation Lecture Eleven Turning Point As we have mentioned, the WKB approximation is useful in problems of wave propagation. In
http://ocw.mit.edu/courses/mathematics/18-305-advanced-analytic-methods-in-science-and-engineering-fall-2004/lecture-notes/eleven.pdf

Complex WKB Solutions and Hamiltonian Systems on Riemann Surfaces pdf

Complex WKB Solutions and Hamiltonian Systems on Riemann Surfaces

Book 6.77 MB | Ebook Pages: 83
(see Ablowitz and Segur [1981]) for small>. and show that it coincides with the WKB approximation for the usual SchrOdinger equation (2.1). Then we will establish a link
http://www.hpl.hp.com/techreports/95/HPL-BRIMS-95-02.pdf

Ch09 Approximate solutions pdf

Ch09 Approximate solutions

Book 4.86 MB | Ebook Pages: 168
and Brillouin (1926) and is called the WKB method or WKB approximation. This method provides approximate wave functions in one-dimensional problems.
http://www.ecse.rpi.edu/~schubert/Course-ECSE-6968 Quantum mechanics/Ch09 Approximate solutions.pdf

Complex WKB Approximations in Graphene Electron-Hole Waveguides in pdf

Complex WKB Approximations in Graphene Electron-Hole Waveguides in

Book 5.34 MB | Ebook Pages: 197
method of Gaussian beams summation is efficient for construction of WKB approximation descriBing electron-hole motion in magnetic field and any scalar potential
http://cdn.intechweb.org/pdfs/19779.pdf

Chapter 11 WKB and the path integral pdf

Chapter 11 WKB and the path integral

Book 6.77 MB | Ebook Pages: 108
The original application of the WKB approximation is the derivation of the Bohr–Sommerfeld quantization condition. If we begin our considerations, for simplicity, with
http://hep.itp.tuwien.ac.at/~kreuzer/qt11.pdf

1 Resonant tunneling structures pdf

1 Resonant tunneling structures

Book 3.24 MB | Ebook Pages: 101
(0) e ( ) (0) e h The tunneling probability in the WKB approximation is given by: ∫ [] = = B ∗ 0 – L 2 –1 2 ( )– d x m U x E x T e h
http://www.ecse.rpi.edu/~schubert/Course-ECSE-6290 SDM-2/1 Resonant tunneling structures.pdf

Tunneling in III-V Nitrides pdf

Tunneling in III-V Nitrides

Book 3.62 MB | Ebook Pages: 192
coefficient is calculated for interband tunnel diode using WKB approximation by potential barrier method and E-k diagram. In order to get substantial amount of tunneling
http://www.nd.edu/~djena/ee87024/report1st_kamal_satyaki_jai.pdf

Wave Reflection over Slowly Varying Bathymetry modeled by pdf

Wave Reflection over Slowly Varying Bathymetry modeled by

Book 4.48 MB | Ebook Pages: 160
The comparison between the analytIcal solution of Reflection WKB approximation with the numerical solution is shown in fig. (4)-(5). The total simulation time is 25 minutes.
http://wwwhome.math.utwente.nl/~kristinaw/poster woudschoten.pdf

Spectral properties of solutions of hypergeometric-type pdf

Spectral properties of solutions of hypergeometric-type

Book 5.91 MB | Ebook Pages: 249
This study will be done within the so-called semiclassIcal (or WKB) approximation [7, 10, 14]. As it is described in Section 2, a recent result [2] based on this method
http://dmaii.etsii.upm.es/~azarzo/downloads/1992_10C.pdf

G.P.Gilfoyle Physics Department University of Richmond, Virginia pdf

G.P.Gilfoyle Physics Department University of Richmond, Virginia

Book 2.1 MB | Ebook Pages: 67
and ¯h is Planck’s constant divided by 2π. Potential barriers of arbitrary shape are then treated using the Wentzel, Kramers, Brillouin (WKB) approximation.1−7 This
https://facultystaff.richmond.edu/~ggilfoyl/qm/AlphaDecayPaper.pdf

Instructor: Phone: Email: TA pdf

Instructor: Phone: Email: TA

Book 5.25 MB | Ebook Pages: 173
• apply several techniques such as perturbation theory, WKB approximation and adiabatic approach to study quantum particles under external fields
http://faculty.ucmerced.edu/ltian/Teaching_Phys_137.pdf

The mode-coupling Liouville Green approximation for a two pdf

The mode-coupling Liouville Green approximation for a two

Book 3.34 MB | Ebook Pages: 137
The Liouville–Green @or Wentzel–Kramers–Brillouin ~WKB!# approximation for the two-dimensional cochlear mechanics problem disagrees with the finite-difference
http://www.lloydwatts.com/JAS02266.pdf

Free electron lasers with slowly-varying beam and undulator parameters pdf

Free electron lasers with slowly-varying beam and undulator parameters

Book 5.53 MB | Ebook Pages: 74
and undulator parameters is developed using the WKB approximation. The the-ory is applied to study the performance of a self-AMPLifled spontaneous emission
http://www.slac.stanford.edu/pubs/slacpubs/10750/slac-pub-10863.pdf

Direct tunneling hole currents through ultrathin gate oxides in pdf

Direct tunneling hole currents through ultrathin gate oxides in

Book 3.43 MB | Ebook Pages: 237
probability.6–8,12,18 In the WKB approximation, it is crucial to use an appropriate hole dispersion in the SiO2 band gap. All previous Models assume a parabolic dispersion
http://www.ece.nus.edu.sg/stfpage/elelimf/publication/Hou YT DT-JAP 02.pdf

Effect of radiation losses on hotspot formation and propagation in pdf

Effect of radiation losses on hotspot formation and propagation in

Book 5.05 MB | Ebook Pages: 247
expected from the nature of the WKB approximation. On the other hand, it can be seen from Fig. 3(a) tha the agreement is uniform over a wide range of values
http://www.maths.ed.ac.uk/~noel/imatimcathymicro.pdf

WORMHOLES WITH A PAST* pdf

WORMHOLES WITH A PAST*

Book 4.39 MB | Ebook Pages: 175
For a euclidean solution to represent a WKB approximation of a tunneling between two classIcally allowed regions, the euclidean
http://neurotheory.columbia.edu/~larry/AbbottNP90.pdf

No-sticking effect and quantum reflection in ultracold collisions pdf

No-sticking effect and quantum reflection in ultracold collisions

Book 4.86 MB | Ebook Pages: 161
feet of the WKB approximation, which breaks down in the long-range attractive part of the potential at low energy. Very far out, the WKB is good even for low energy
http://monsoon.harvard.edu/papers/mody2001.pdf

Q u an tu m M ech an ics pdf

Q u an tu m M ech an ics

Book 5.05 MB | Ebook Pages: 177
We can make life a bit easier by using the quantization condition derived from the WKB approximation. Since we require the wavefunction to vanish exactly at x= 0, we have:
http://k2.chem.uh.edu/quantum/Notes/versions/QC-v5.pdf

PHY 407 QUANTUM MECHANICS Fall 05 Problem set 1 Due Sep 15 2005 pdf

PHY 407 QUANTUM MECHANICS Fall 05 Problem set 1 Due Sep 15 2005

Book 2.67 MB | Ebook Pages: 182
Use the WKB approximation to find a formula for the number of bound states of energy less than E. In particular, estimate the total number bound states ( i.e., the number
http://www.pas.rochester.edu/~rajeev/phy407/problems.pdf

Asymptotic iteration method applied to bound-state problems with pdf

Asymptotic iteration method applied to bound-state problems with

Book 1.72 MB | Ebook Pages: 243
One of the methods mentioned above, the WKB approximation, is for solving the SchrOdinger equation by expanding the wave function in the power series of¨ ~.
http://www.nipne.ro/rjp/2012_57_3-4/0582_0593.pdf

Electron tunneling through the repulsive Coulomb barrier in pdf

Electron tunneling through the repulsive Coulomb barrier in

Book 1.72 MB | Ebook Pages: 100
The observed tunneling effect and spectral shift are explained using WKB 22n2 approximation based on a Model potential with a square well at short range and a repulsive
http://users.tricity.wsu.edu/~physics/publication/PDF/Electron Tunneling through the Repulsive Coulomb Barrier in Photodetachment of Multiply Charged Anions.pdf

Quantum Mechanics - II PHYS 4308 pdf

Quantum Mechanics - II PHYS 4308

Book 2.29 MB | Ebook Pages: 62
common and powerful tools in quantum mechanics and will be studied next. The WKB approximation will be followed by time-dependent perturbation theory where we will cover
http://www.phys.ttu.edu/~slee/courses/physics_courses_files/2010_spring/syllabus/S10_4308_Akchurin.pdf

Analytical Models for Quantized Sub-Band Energy Levels and pdf

Analytical Models for Quantized Sub-Band Energy Levels and

Book 1.43 MB | Ebook Pages: 122
(17) to determine the WKB integral I values in (14) gives a better result compare to the triangular approximation at strong inversion region. Figure 2 shows the numerIcal
http://www.cgu.edu/include/191.pdf

Quantum Picture of the Josephson Junction pdf

Quantum Picture of the Josephson Junction

Book 7.15 MB | Ebook Pages: 157
The results match the results from WKB approximation with 3 TT21/~10 and 2 TT32/~10, but 2 TT10/~10in this calculation is slightly different from
http://www.physics.drexel.edu/~bob/Term_Reports/Junction_YY.pdf

Nanofocusing of Optical Energy in Tapered PlasmonicWaveguides pdf

Nanofocusing of Optical Energy in Tapered PlasmonicWaveguides

Book 1.72 MB | Ebook Pages: 233
equations in eikonal (WKB) approximation in the form: E z r;z R r I 0 k 0 mr r R BK 0 k 0 dr ;E z r; z R r i n m I 1 k 0 mr r R i n d BK 1 k 0 dr ; (4) where B I
http://www.phy-astr.gsu.edu/stockman/data/Phys_Rev_Lett_93_137404_2004_Nanofocusing_in_Tapered_Plasmonic_Waveguides.pdf

Modeled Tunnel Currents For High Dielectric Constant Dielectrics pdf

Modeled Tunnel Currents For High Dielectric Constant Dielectrics

Book 4.48 MB | Ebook Pages: 234
using the WKB approximation as [2], [13] (6) where is the insulator effective mass which is assumed constant. The integration in (6) is over all real values of
http://repository.lib.ncsu.edu/publications/bitstream/1840.2/458/1/lucovsky_1998_ieee_trans_electron_devices_1350.pdf

Year 1 Progress Report for NASA AISR Grant NNG04GP83G: A Numerical pdf

Year 1 Progress Report for NASA AISR Grant NNG04GP83G: A Numerical

Book 4.67 MB | Ebook Pages: 197
The FDTD scattering component and the WKB-approximation propagation component were combined to calculate the reflected signals received by orbital GPR.
http://aisrp.nasa.gov/projects/reports/106754ff020.pdf

Physics 216. Quantum Mechanics. Professor Dine Spring, 2004. Syllabus pdf

Physics 216. Quantum Mechanics. Professor Dine Spring, 2004. Syllabus

Book 5.34 MB | Ebook Pages: 103
The WKB approximation, tunneling, perhaps a little bit of path integration. (Shankar 16, Sakurai 5.4, also pp. 104-109 from chapter 2. Supplementary handouts).
http://scipp.ucsc.edu/~dine/ph216/216_syllabus04.pdf

9 Reflection, Absorption, and Mode Conversion pdf

9 Reflection, Absorption, and Mode Conversion

Book 4.29 MB | Ebook Pages: 127
When k2(x) is slowly varying, i.e., |k′′| ≪ |kk′| and |k′| ≪ |k2|, the WKB approximation can be used. The solution is given by E = (const.
http://fusion.k.u-tokyo.ac.jp/~takase/plasma1_ch9.pdf

Coherent and Incoherent Scattering by Oceanic Bubbles pdf

Coherent and Incoherent Scattering by Oceanic Bubbles

Book 3.91 MB | Ebook Pages: 150
rays, a straightforward application of the lowest-order WKB approximation to the Helmholtz equation (1) for the coherent field (p) generated by a unit point source
http://sarkar.me.udel.edu/pdf/JASA_94.pdf

Tunneling in long-wavelength infrared HgCdTe photodiodes pdf

Tunneling in long-wavelength infrared HgCdTe photodiodes

Book 6.39 MB | Ebook Pages: 158
lated from the WKB approximation.The barrier height is the bandgap for BTB, 1 whereasinTAT calculations it is determined by the energies of trap states.
http://aristotle.sri.com/srini/68-JEM.pdf

Modeling CMOS tunneling currents through ultrathin gate oxide due

Book 1.62 MB | Ebook Pages: 242
the WKB approximation [11], Schuegraf et al. have derived a simple analytIcal formula to represent direct-tunneling through a trapezoidal barrier [1], [2].
http://www.eecs.berkeley.edu/~hu/PUBLICATIONS/PAPERS/729.pdf

IEEE Electron Device Letters

Book 6.39 MB | Ebook Pages: 216
can be estimated using the WKB approximation [15], [16]. - (1) where and are the respective widths of sub-oxide regions (in Å) with and without Interface nitridation, and
http://www.physics.ncsu.edu/u4a/papers/ncsu/SiOxNy.pdf

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