What is Potential barrier: Definition and 83 Discussions

In quantum mechanics, the rectangular (or, at times, square) potential barrier is a standard one-dimensional problem that demonstrates the phenomena of wave-mechanical tunneling (also called "quantum tunneling") and wave-mechanical reflection. The problem consists of solving the one-dimensional time-independent Schrödinger equation for a particle encountering a rectangular potential energy barrier. It is usually assumed, as here, that a free particle impinges on the barrier from the left.
Although classically a particle behaving as a point mass would be reflected if its energy is less than



{\displaystyle V_{0}}
, a particle actually behaving as a matter wave has a non-zero probability of penetrating the barrier and continuing its travel as a wave on the other side. In classical wave-physics, this effect is known as evanescent wave coupling. The likelihood that the particle will pass through the barrier is given by the transmission coefficient, whereas the likelihood that it is reflected is given by the reflection coefficient. Schrödinger's wave-equation allows these coefficients to be calculated.

View More On Wikipedia.org
  1. Rhdjfgjgj

    Potential barrier problem in mechanics

    Here our sir said if I would apply energy conservation b/w initial point and B , we would get it wrong. But If I apply between initial point and D , we would get it right. He didn't tell why. Could anyone just explain why. One reason I thought was that since the question asked for minimum...
  2. ValeForce46

    I Separation energy of nucleons and Coulomb barrier

    My professor and the book I'm reading (Particles and Nuclei: An Introduction to the Physical Concepts by Povh et al.) says that "The emitted nucleons are primarily neutrons since they are not hindered by the Coulomb threshold" which means that a neutron has a separation energy lower than a...
  3. M

    I Potential step and tunneling effect

    We know that thanks to the tunnel effect, in the case of a finite potential step (V) and considering a stationary state, when a plane wave with energy E < V encounter the step the probabability that the wave-particle coming from -∞ (where potential is V=0) will be ≠ 0, in particular the wave...
  4. Leonardo Muzzi

    I Can an electron quantum tunnel inside the potential barrier?

    When I see explanations for quantum tunneling, the discussion is around the probability of an electron manifesting itself before the potential barrier, and after the potential barrier. However, looking at the curves draw, there is a non-zero probability (the evanescent part of the wave) inside...
  5. T

    Quantum tunneling: T(E) graph for a potential barrier diagram

    This is the V(x) diagrams and what I am thinking (really not sure though) is that for the first one you the energy has to reach V2 before it can start transmitting and the graph can take off from T=0, since there is an increase in energy potential that is V2. And as the energy increases, the...
  6. Haynes Kwon

    I Probability flux inside the finite potential barrier

    In Bransden textbook, it is stated that the probability current density is constant since we are dealing with 1-d stationary states. It gives probability flux outside the finite potential barrier which I verified to be constant with respect to x, but it doesn't provide the probability current...
  7. J

    Finding the expected value of position in a Potential Well

    Homework Statement Hello today I am solving a problem where an electron is trapped in a potential well. I have a solved Schrodinger's Equation. I am having problems in figuring out what the wave function should be. When I solved the equation I got a complex exponential. I know I cannot use the...
  8. Clara Chung

    I Question about the solution of TISE (finite potential barrier)

    Let's say the solution on the left hand side is a sinkx + b coskx = 0 We get one solution for each E if we omitted a and another solution if we omitted b. However, how to conclude that they are all the solutions? Will there be any solution of the 5 coefficients such that a and b are both not...
  9. M

    Quantum mechanics: potential steps

    Homework Statement The Attempt at a Solution [/B] Hi All, I'm having trouble answering part (f) of the above question. I have managed parts (d) and (e) fine but am not sure how to proceed with part (f). I am pretty sure that the amplitude of the reflected wave in region 1 will be zero...
  10. B

    I Tunneling through a finite potential barrier

    I have 3 questions. After thinking about it I feel these questions may indicate that I have some misunderstanding in basic knowledge or some missed parts. 1. Why is the (time independent) wavefunction an exponential decay inside the potential barrier? I know the mathematical derivation, but I am...
  11. E

    Probability of penetrating a potential barrier

    Homework Statement The probability for a particle of energy E<<V0 to penetrate a potential barrier of height V0 and width d is approximately \frac{16E}{V_0}exp\left[\frac{-2d\sqrt{2m(V_0-E)}}{\hbar}\right]. An electron moves between two potential barriers of height V0 and 2v0 that are of widths...
  12. D

    I Does a Delta Potential Barrier Allow for Bound Solutions?

    Hi. I understand that in 1-D when E< V(minimum) there exist no physically acceptable solution to the Schrodinger Equation. I have been looking at delta potentials using Griffiths book. I follow his working for the delta potential well but when it comes to the potential barrier I don't understand...
  13. S

    Infinite Square Well, Potential Barrier and Tunneling

    Homework Statement Consider a one-dimensional, non-relativistic particle of mass ##m## which can move in the three regions defined by points ##A##, ##B##, ##C##, and ##D##. The potential from ##A## to ##B## is zero; the potential from ##B## to ##C## is ##\frac{10}{m}\bigg(\frac{h}{\Delta...
  14. S

    Centrifugal term in mechanical energy in gravitation

    I'm studying effective potential in Newtonian gravitation. The mechanical energy of a body can be written $$E=\frac{1}{2}\mu {\dot{r}}^2+\frac{L^2}{2\mu r^2}-\gamma \frac{m M}{r^2} \tag{1}$$ Where \mu is the reduced mass of the system planet-star. Consider now the term...
  15. I

    Potential barrier, reflection coefficient

    Homework Statement Electrons are pushed into a grounded metal tube A by the kinetic energy of 100 eV. After having gone through the tube it passes into another tube, B, at some distance from A. Tube B is kept at a potential of -50V. Calculate how many of the electrons are reflected back into...
  16. Chip

    Penetrating the Rectangular Potential Barrier, E < V0

    The following code compares my result to the known correct result. Can anyone find where my error is? If you run the octave code you will see that my answer has positive concavity whereas the correct one has negative concavity...I've checked this so many times and can't find my error. I wanted...
  17. Chip

    Penetrating the Rectangular Potential Barrier, E < V0

    Homework Statement Rectangular barrier of width a and height V0 with an E < V0. What is the transmission ratio, T? Homework Equations T = C*C/A*A What am I missing in my attempted solution (variable name = TChip), which is different from the known solution (variable name = TSoln)? The Attempt...
  18. H

    100% transmission through a potential barrier

    A particle of energy ##E## is incident upon a potential barrier of potential ##V_0## and of thickness ##a##. Given that ##E>V_0##, the transmission coefficient is given by If destructive interference occurs when the path difference between the two reflected waves (at points ##x=0##...
  19. I

    What does the potential barrier energy measure?

    The energy of an incident charged particle refers to its kinetic energy. What does the potential barrier energy refer to qualitatively? EDIT: Is it just in reference to the "potential barrier" in the classical sense? where if the particle has less than the energy V, then it doesn't go through...
  20. Summer95

    Algebra in potential barrier problem

    Homework Statement It is a potential barrier with E of the incoming matter wave E>U (greater than the height of the barrier). I have already done a LOT of algebra to get to the point where ##\frac{F}{A}=\frac{2kk'e^{-ikL}}{2kk'cos(k'L)-i(k'^{2}+k^{2})sin(k'L)}## which I won't bother writing...
  21. D

    Particle waves through a potential barrier

    Hi all, I came across this figure in a textbook. Simple stuff, but can get tricky: I don't understand why the sign convention flips upon entering the barrier (region II), but I guess the book is correct and that I should just take it as a fact. If anybody has a reasonable thought to add...
  22. Joy Prakash Das

    Wave function for a potential barrier

    Suppose I have a region from 0 to L. I have a barrier potential V from x1 to x2, such that 0<x1<x2<L. The potential is 0 everywhere. I have obtained the wave-function by considering the propagation from left to right. Now if I consider the propagation from right to left should I get a different...
  23. B

    Transmission Coefficient for Quantum Barrier

    Homework Statement Picture of Problem: Homework Equations $$\psi(x) = A_n e^{ikx} + B_n e^{-ikx}$$ for n=1,2,3 The Attempt at a Solution I know i need to relate the wave functions $$A_n e^{ikx} + B_n e^{-ikx}$$ for n=1,2,3 (the three areas of the barrier - before barrier, inside barrier...
  24. X

    What is potential barrier against the photon penetration

    It is known that the penetration depth of photon into a material depends on the energy of the photon, density and atomic number of the material; because the photon energy is normally smaller than the potential against the penetration of photon, which is the potential barrier, so the incident...
  25. G

    Rectangular Potential Barrier Boundary Conditions with E=V

    Homework Statement I am trying to calculate the transmission and reflection coefficients for rectangular finite potential barrier between (-a, a) for a particle of mass m with energy equal to the height of the barrier (E = V0 > 0). Homework Equations...
  26. K

    Quantum physics potential barrier R and T

    Homework Statement Prove (6-44) which expresses the reflection and transmission coefficients in terms of the ratio E/V0.Homework Equations [/B] The Attempt at a Solution express k1 and k2 in terms of V/E? [/B]
  27. kq6up

    Delta Function Potential Barrier

    Homework Statement Background: The problem is to find the uncertainty relationship for the wave equation for a delta function potential barrier where ##V(x)=\alpha\delta(x)##. Check the uncertainty principle for the wave function in Equation 2.129 Hint: Calculating ##\left< p^2 \right> ##...
  28. J

    Potential Barrier for different types of junctions

    Hi all, How I can calculate the Potential Barrier when we have a metal- semiconductor, metal- metal, or p-n junction ? Can I calculate the Potential Barrier by using a workfuncion?
  29. L

    Potential barrier. Schroedinger equation.

    Homework Statement Schroedinger equation for potential barrier. What if ##V_0=E## First region. Particles are free. ##\psi_1(x)=Ae^{ikx}+Be^{-ikx}## In third region ##\psi_3(x)=Ce^{ikx}##Homework Equations ##\frac{d^2\psi}{dx^2}+\frac{2m}{\hbar^2}(V_0-E)\psi=0## where ##V_0## is height of...
  30. R

    Help with Potential Barrier question

    I have always understood (As well as I can) potential barrier questions, but this one has stumped me, and I was hoping someone could point out where my thinking has gone wrong. The wave function of an electron of mass m incident to the step from x = -∞ with energy E < V is = eikx + ρe-ikx for...
  31. M

    Solving Schrod. Eqn. for Potential Barrier with E > V

    I have a question that's driving me insane and I'm sure there's a simple answer that I'm missing for some reason, but I'm not getting my a-ha moment. Consider 2 cases from intro QM: Infinite square well Potential barrier with E > V0 For the infinite square well, the Schrodinger eqn...
  32. H

    Number of standing waves in a potential barrier

    Homework Statement Consider a resonant tunneling diode structure (attached image). This shows 2 AIAs barriers of height 1.2 eV and width t = 2.4 nm, enclosing a well of width L = 4.4 nm. If the effective mass of the electron is taken as 0.9 times the free electron mass how many separate...
  33. H

    Possible Rectangular Potential Barrier Transmission Problem

    1. The Problem Statement An electron of effective mass m* = 0.2me and energy E = 0.1 eV hits a barrier of height 0.4 eV and width t = 5 nm. What is the probability of transmission through the barrier? Use the simplest estimate which is an exponential function. Homework Equations I think...
  34. Z

    Eigenfunction & Potential Barrier

    Homework Statement A particle of total energy E is incident on a potential barrier V0 (E<V0) between x=0 and x=a. Write down the allowed eigenfunctions in the regions x<0, 0<x<a and x>a in terms of five unknown constants A, B, C, D and F where A and F are the amplitudes of the incident and...
  35. A

    Alpha decay potential barrier.

    Homework Statement A nuclei of a atomic number Z decays into a alpha particle (a He nucleus with Z =2) and a daughter nucleus with (Z_{d}). The decay may be described as the tunneling of an alpha-particle through a barrier caused by the Coulomb potential between the daughter and the...
  36. dexterdev

    Conceptual difference between potential barrier & potential difference

    Hi PF, What is the conceptual difference between potential barrier and potential difference? both have an electric field associated with it. so is potential barrier a sort of potential difference itself and will it cause current flow in a closed circuit like diode shorted. Also why cannot we...
  37. J

    Potential Barrier help starting problem

    Homework Statement Infinite Potential Barrier particle moving in one dimension is incident upon a potential barrier given by V (x) = Gδ(x) where δ(x) is the Dirac delta function and G is a constant with units of energy times distance. (The delta function must have units of inverse distance...
  38. Y

    Who does or sees an experiment on rectangluar potential barrier?

    In QM textbook, there is the solution of shroedinger Eq. on the rectangular potential barrier. The reflection rate can be caculated in each case, E>V0, E=V0 and E<V0. But, I can't find the experiment on the rectangular potential barrier anywhere. Is there anybody who does or sees such an...
  39. R

    Potential Barrier (quantum mechanics)

    Homework Statement I need help with part (iii) and (ii) of the follwoing problem: http://img228.imageshack.us/img228/516/79620850.jpg Homework Equations From my notes transmission coefficient for E<U is: T(E)= \left[ 1+\frac{1}{4} \left( \frac{U^2}{E(U-E)} \right) sinh^2 (\alpha L)...
  40. J

    Description of a wave packet incident on a square potential barrier

    A wave packet of mean energy E0 is incident on a potential square barrier. The figure below shows stills from a film showing 9 successive stages in interaction. a) True or false? The incident packet at time t = 0 describes many particles, each in a different momentum state. If false, tell...
  41. A

    Calculation of ion flux across potential barrier

    Hello! As far as I know, the Eyring equation is used to calculate the speed of a reaction: k=\frac{{k}_{b}}{h} {e}^{\frac{-\Delta G}{RT}} In my course the teacher used this formula to calculate the flux of a species of ions across a barrier of potential, but I didn't understand very...
  42. fluidistic

    Potential barrier in QM problem with coefficient of transmission

    Homework Statement I'll try to recreate from my memory the problem we've been assigned on a test more than one month ago. They gave the solution but I either misunderstood or miscopied it. An electron with kinetic energy 5 eV goes from a region with potential V_0=6 eV (let's call this region...
  43. fluidistic

    Quantum mechanics, potential barrier

    Homework Statement A particle of mass m goes toward the unidimensional barrier potential of the form V(x)=0 for x\leq 0 and a\leq x and V(x)=V_0 for 0<x<a. 1)Write the corresponding Schrödinger's equation. 2)Calculate the transmission coefficient for the cases 0<E<V_0 and E>V_0. Hint: Check...
  44. G

    Rectangular Potential Barrier Where E=V0

    Homework Statement V(x) = 0 for x < 0; V0 for 0 < x < a; 0 for x > a Particle of mass m E=V0 Asks for general solution and transmission coefficient. Homework Equations Time-Independent Schrodinger Equation The Attempt at a Solution I've found region I (the left region where x <0) to be...
  45. M

    Transmission and reflection coefficients for potential barrier

    Homework Statement An electron with kinetic energy 5 eV (8.01E-19 J) passes through a 3 eV (4.806E-19 J) potential barrier. There are certain widths for this potential barrier in which the transmission probability will equal one hundred percent and the reflection probability will equal zero...
  46. O

    Potential barrier of Silicon Diode

    As we know the potential barrier of silicon diode is 0.7V at "Normal Temperature" But if the Temperature is 120 degree Centigrade then what will happen? 1) the Potential Barrier will increase 2) Decrease 3) Remain Same Please Explain also!
  47. X

    Infinite potential barrier question.

    Homework Statement I'm asked to calculate the reflection and transmission coefficients for scattering from a potential energy barrier. The potential energy barrier is, V(x)=\frac{\hbar^2}{2m} \frac{\lambda}{b} \delta(x) where \delta (x) is the Dirac delta function. Homework Equations See...
  48. P

    Solving Quantum Mechanical Potential Barrier Problem

    Hi! I'm struggeling with a quantum mechanical problem. Homework Statement An alpha-particle is "trapped" inside a uraniumcore, and the potential is simplified to 0 for R2 < r V0 for R1<= r <= R2 0 for 0<= r < R1 I have calculated the transmission coefficient T =...
  49. R

    Potential step with infinite potential barrier (D.A.B Miller problem 2.8.6)

    Homework Statement We have a potential structure as follows: from z=negative infinity to z=-b, the potential is 0. At z=-b, the potential jumps up to some V_0. Then, at z=0, there is a potential barrier of infinite height. I need to solve for the magnitude of the reflected wave (i.e. the wave...
  50. Z

    Potential barrier problem

    Homework Statement a particle of kinetic energy E is incident from left on a potential barrier,height U, situated at the origin.the barrier is infinitely wide and E>U obtain an expression for the reflection coefficient R of the particle as a fuction ratio e=E/U Homework Equations...