Wkb Definition and 27 Threads

hello everyone I tell you a little about my situation. I already found the approximate wavefunctions for the schrodinger equation with the potential ##V(x) = x^2##, likewise, energy, etc. I have the approximate WKB solution and also the exact numeric solution. What I need to do is to calculate...

In Zettili book, it is given that ## \nabla^2 \psi \left( \vec{r} \right) + \dfrac{1}{\hbar ^2} p^2 \left( \vec{r} \right) \psi ( \vec{r} ) =0 ## where ## \hbar## is very small and ##p## is classical momentum. Now they assumed the ansatz that ## \psi ( \vec{r} ) = A ( \vec{r} ) e^{i S( \vec{r} )...

Homework Statement: The Task is to calculate the Transmission coefficient with the WKB Approximation of following potential: V(x) = V_0(1-(x/a)²) |x|<a ; V(x) = 0 otherwise Homework Equations: ln|T|² = -2 ∫ p(x) dx I have inserted the potential in the equation for p(x) and recieved p(x) =...

If it is the asymptotic behavior of the Airy's function what it's used instead of the function itself: Does it mean that the wkb method is only valid for potentials where the regions where ##E<V## and ##E>V## are "wide"?

In order to use WKB approximation, the potential has to be "slowly varying". I learned the method from this video: But the Professor hasn't mentioned in detail what the measure of "slowly varying" is. What is the limit beyond which we cannot use the WKB method accurately?

What is the nonperturbative approach to quantum mechanics as opposed to perturbative one? When does the latter method fail and one has to apply nonperturbative approach? Please keep your discussion confined within non-relativistic quantum mechanics.

According to WKB approximation, the wave function \psi (x) \propto \frac{1}{\sqrt{p(x)}} This implies that the probability of finding a particle in between x and x+dx is inversely proportional to the momentum of the particle in the given potential. According to the book, R. Shankar, this is...

Homework Statement Good day all! I'm studying for finals and i'd like to know how to do this problem (its not homework): "Using the WKB method, find the bound state energies E_n of a particle of mass m in a V-shaped potential well: V(x)= \begin{Bmatrix} -V_0 (1- \begin{vmatrix}...

Any good book for starting wkb approximation except Griffth... Please suggest some...

Consider E>V(x). WKB states the wavefunction will remain sinusoidal with a slow variation of wavelength $ \lambda $ and amplitude given that V(x) varies slowly. From the equation \begin{equation} k(x)=\frac{\sqrt{2m(E-V(x))}}{\hbar} \end{equation}, I can see that the k(x) is directly...

I'm trying to understand why the WKB approximation doesn't seem to work in the following case. Suppose you have a particle of mass ##m## in a potential ##V(x)=q m\cos(2mx/\hbar)##, where ##q\ll 1##. Consider then the stationary solution with energy ##E=m/2##. The Schroedinger equation is then...

1. Consider a quantum well described by the potential v(x)=kx^{2} for \left|x\right|<a and v(x)=ka^{2} for \left|x\right|>a. Given a^{2}\sqrt{km}/\hbar =2, show that the well has 3 bound states and calculate the ratios between the energies and ka^{2}. You may use the standard integral...

Hi everyone, I was wondering if you guys could suggest me some good books in cosmology with finely explained WKB method and Perturbations especially in Structure formation area. I have "The early universe" by Klob and Turner and "Cosmology" by Weinberg , but they seem unpalatable at first...

Hello, I'm trying to solve for the allowed energies with the WKB approximation of the Schrodinger equation, using the Morse potential. So I have (as per equation 35 at http://hitoshi.berkeley.edu/221a/WKB.pdf), \int_a^b \sqrt{2m(E-V(x))}dx=\left(n+\frac{1}{2}\right)\pi\hbar However, how do I...

i think every system is accurately described by Schrodinger equation. so what is the point of using old quantum mechanics methods? with Schrodinger equation, at least numerically, you can solve the eigenvalues and eigenvectors readily and accurately. So what is the point of using...

Hi, I have been looking for rigorous mathematical conditions for when the WKB approximation may be applied. Here is my understanding of the topic. We start with the most general form that the wavefunction could take, i.e. exp[if(x)/h] , Where "i" stands for square root of -1, f(x) is...

let x be the parameter in some interval and let lambda tend to infinity. Should I treat x as of the same order as constants, i.e x=O(1)?

problem with integration for WKB approximation in MATLAB hi all, i have been having troubles with getting MATLAB to solve the following problem (the language is not the MATLAB one, the functions are not solvable by the symbolic integration and i was trying to get one of the quad functions to...

Dear All, I have recently read about WKB approximation and about perturbation theory. Both methods are applicable in the range of slowly varying potentials. What I have not understood is which is the range of applicability of one of the method compared with the other one. More...

Hi, Why is it that the WKB approximation produces the correct eigenvalues for the Harmonic Oscillator problem, but the wrong wavefunctions, whereas for the square well, we get correct wavefunctions and the wrong eigenvalues? I've been trying to dig through the approximations we make in...

WKB theory?? Pls help Homework Statement WKB theory and WKB approximation. Are they same?? Homework Equations I have to do a presentation about WKB theory in Physics (Quantum mechanics) but I don't know how to start from the WKB theory and come to WKB approximation. i.e. I don't find a...

Hi, This is just a quick question -- I'm puzzled by the way this answer sheet represents the potential function. The question asks us to determine the energy eigenvalues of the bound states of a well where the potential drops abruptly from zero to a depth Vo at x=0, and then increases...

Hi all I have a question about WKB approximation Why is it that WKB method can be applied only to problems that are one dimensional or those which can be reduced to forms that are one dimensional ones? any help is deeply appreciated

for a Hamiltonian H=H_0 + \epsilon V(x) my question is (for small epsilon) can WKB and perturbative approach give very different solutions ?? to energies eigenvalues and so on the index '0' means that is the Hamiltonian of a free particle. problem arises perhaps in calculation of...

Hey! In deriving the WKB approximation the wave function is written as \psi \left( x \right) = exp\left[ i S\left( x \right) \right ] Now, in some of the deriviations I've seen, the function S(x) is expanded as a power series in \hbar as S(x) = S_0(x) + \hbar S_1(x) +...

let,s suppose we have a particle with mass m\rightarrow\infty then my question is if would be fair to make the WKB approach by setting the solution of the Schroedinguer equation as \phi=e^{iS/\hbar} wiht S hte classical action satisfying the equation: (dS/sx)^{2}+2m(V(x)-E_{n})=0 with E_n...

Consider the potential V(x) = \beta x for x \geq\ 0 V(x) = 0 for x < 0. Find the exact and WKB wavefunction for the situation where a particle has E = 10 in units where \beta = \hbar = m = 1. Any suggestions guys? James