What is Step potential: Definition and 37 Discussions

In quantum mechanics and scattering theory, the one-dimensional step potential is an idealized system used to model incident, reflected and transmitted matter waves. The problem consists of solving the time-independent Schrödinger equation for a particle with a step-like potential in one dimension. Typically, the potential is modelled as a Heaviside step function.

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  1. E

    Electron encountering metal surface (1D Step potential)

    I am struggling with how to go about this; in particular, I'm not sure I understand what state is being alluded to when Ballentine says "For an electron that approaches the surface from the interior, with momentum ##\hbar k## in the positive ##x## direction, calculate the probability that it...
  2. R

    Penetration depth and step potential

    Homework Statement I am trying to figure out the average penetration depth into a finite step potential, similar to this thread: https://www.physicsforums.com/threads/qm-barrier-penetration.104641/ But instead of just estimating the depth as ##\frac{1}{\kappa}##, i would like to calculate it...
  3. O

    Step potential, continuous wave function proof

    Homework Statement I am being asked to show that the wave function ψ and dψ/dx are continuous at every point of discontinuity for a step potential. I am asked to make use of the Heaviside step function in my proof, and to prove this explicitly and in detail. Homework Equations...
  4. D

    Boundary conditions for a step potential

    Homework Statement A particle with mass m and spin 1/2, it is subject in a spherical potencial step with height ##V_0##. What is the boundary conditions for this eigenfunctions? Find the degeneracy level for the energy, when it is ##E<V_0## Homework Equations Radial equation \begin{equation}...
  5. Docdan6

    Classical behavior, 3 dimension wave function and reflection

    Homework Statement I'm a pharmacologist and I have a modern physics course to do. This is not my field and I'm completely lost... We were given this problem to do. Thanks a lot in advance. Consider a potential where U(x) = 0 for x ≤ 0 U(x) = -3E for x > 0 Consider a particle of energy E...
  6. elanier

    Step Potential Transmission Probability as t->inf

    At t=0 we have a particle incident from the left on a step potential (where V(x) = V0 for x ≥ 0 and V(x) = 0 otherwise). The particle has energy of 5/4 V0 and the question asks to find the probability that it will be on the right (ie. x > 0) as t→∞. I understand how to solve this problem and...
  7. Guaicai

    Scattering in Finite step potential

    origin page : http://www.physicspages.com/2012/08/08/finite-step-potential-scattering/ No quite understand how the solution come from this equation
  8. A

    Schrodinger equation for step potential

    Homework Statement Consider the one-dimensional Schrodinger equation for the step potential, that is for U(x) = 0 for x<0, and for , . Consider a particle with mass m and energy E < U. Assume the particle is initially at x<0. a) Calculate the penetration depth Δx at which the probability...
  9. J

    QM: Calculate Transmission Coefficient

    Homework Statement V(x) = -V ( if x > 0 ) 0 ( if x <= 0) ( V is positive constant) the transmission coefficient is not simply F2 / A2 ( with A the incident amplitude and F the transmitted amplitude ), because the transmitted wave travels at a different speed. Calculate...
  10. B

    Step Potential with incident and reflected waves

    Homework Statement A woman is walking along a road. She has a mass of 52 kg and is walking at 1 m/s. (a) She is not paying careful attention and is walking straight towards the wall of a nearby building. Assume that the wall is infinitely hard and that she can be described as a plane wave (a...
  11. H

    Physical meaning of solution to step potential with E = V0

    I am able calculate the solution for the TISE relating to the interval to the right of a step potential; however, I am unclear as to what this solutions represents physically for this scattering problem. So, starting with (-ħ2/2m)d2/dx2Ψ2(x) + V(x)Ψ(x)2 = EΨ(x)2 where V(x)Ψ(x)2 =...
  12. H

    No solution with E=v0 for step potential

    Is it the case that there is no general solution for the step potential with E = V0? This seems as though it must be the case as there are only certain energy eigenvalues which would be allowed and, therefore, we cannot for all possible values for the potential barrier find allowed energy...
  13. K

    Heaviside Step Potential - Tunneling

    I'm working on a basic potential step problem from Griffiths QM. Its problem 2.34 in the textbook. I am having trouble understanding the transmission coefficient in this problem. I realize that I can calculate the reflection coefficient and just do 1 minus the result but I am looking for...
  14. bcrowell

    Correspondence principle for a step potential

    Consider the Schrodinger equation with the step-function potential V(x)=\begin{cases} 0, & x<0 \\ U, & x>0 \end{cases}\qquad . A pulse with E>U comes in from the left with unit amplitude and undergoes partial reflection. The reflection has an amplitude (ignoring phase) that is given by the...
  15. F

    Solving Schroedinger Equation for a Step Potential

    Undergraduate Quantum Mechanics problem. However the course hasn't gone as far to include R or T so I'm assuming there must be a way to solve this without needing to know about those. Homework Statement Asked to show that \psi(x)=A\sin(kx-\phi_0) is a solution to the 1D-time-independent...
  16. T

    Normalization of step potential eigenfunction

    Hi, I am stuck with a problem which effectively boils down to this: Given the eigenstates of a Hamiltonian with a step potential in the x direction H=-\hbar^2/2m \nabla^2 + V_0 \Theta(x) \psi(q)_{in}=cos(qx)-\frac{\sqrt{K_{V_0}^2-q^2}}{q}sin(qz) \qquad x<0...
  17. B

    Force of Particle in Step Potential

    Homework Statement We have a particle in a step potential. Consider it as a plane wave traveling left to right and hitting a step potential V at x=0. Assuming it behaves like a fluid, what is the force it exerts on the wall in terms of F'[0], where F'[x] is the derivative of the wave function...
  18. U

    Solving Schroedinger's equation for Step Potential

    Consider the case for a particle with energy E in a region where : V = 0 , x<0; V=Vo, x>0; for the first region when we write Schrodinger’s equation(Time independent) it will be -h^2/2m d2ψ/dx2 = Eψ and for second region it was -h^2/2m d2ψ/dx2 = (Vo-E)ψ; My doubt is that won't...
  19. C

    Quantum Mechanics and the Step Potential: Exploring the Physics of E=U

    I understand the two cases dealt with when we consider the step potential. The two cases being when E>U (i.e the total energy is less than the max potential of the potential barrier) and when E<U. What is the physics of the situation when E=U? Is it a sort of a hybrid situation between the two...
  20. T

    Solving Reflection Coefficient for Step Potential: Why B ≠ 0?

    Homework Statement I'm working through a step potential and I am confused as to why one of the coefficients doesn't go to zero. V(x) = 0 when x < 0; V(x) = V_not when x > 0; a. Calculate reflection coefficient when E < V_not I can solve the reflection part, it is a step towards it...
  21. andrewkirk

    Clear and thorough development of the step potential wave function

    I am reading Shankar's "Principles of Quantum Mechanics" and am up to the part where he uses Schrodinger's equation to derive the wave function for various 'simple' scenarios in one spatial dimension. The first few were fine but his presentation of the step potential problem (specifically...
  22. E

    Step Potential and Wave Functions

    Homework Statement I have a step potential where E < V0. I also have to do this for E >V0 but I think after we do the first part it'll make sense. Plot the behavior of the wave function in crossing the region at x = 0, considering four values of the energy. So I'll end up with four...
  23. Q

    Step Potential Question (Quantum Mechanics)

    Homework Statement Write out the spatial portion of the wavefunction for a particle coming from the right with energy (E) greater than the step potential (U) and passing over the step.Homework Equations The Attempt at a Solution I just want to know if this is the right set of equations for this...
  24. 7

    Transmission of a TWO step potential

    Homework Statement Consider the potential: V(x) =0 x<0 =V1 0<x<a =V2 x>a Where 0<V1<V2 and E>V2 Evaluate the transmission coefficient for the incident wave into the region x>a Homework Equations T= 4k0k1/((k0+k1)^2) The Attempt at a Solution I have not attempted this. It...
  25. L

    Solving the Schrödinger Equation for a Step Potential

    Hi everybody! I'm studying the simple case of the solution of the Schrodinger equation for a step potential "[URL .[/URL] As my professor states , the transmission coefficient is 0 when the energy of the particle is E<V. I really don't get how this result is not a contradiction with the fact...
  26. H

    Reflection coefficient of step potential

    why reflection coefficient R=1 in step potential though there happens transmission also as a negative exponential when E<V0
  27. I

    (simple)Journal Papers using Step Potential

    Homework Statement I am a beginning quantum mechanics student, and I need to solve a journal paper that uses the step potential fairly simply. I've been searching for (literally) days, but everything seems to be far too complicated. Can someone please point me in a direction, or offer some...
  28. T

    Transmission Coefficient for two step potential

    Homework Statement E>V_1 & V_2 So it's a step potential wave, setup. Let's set it up along the x axis. At x=0, there is the first step where it is V_1. At x=a, there is another step, where V_2>V_1. Show that the transmission coefficient is...
  29. T

    Step potential - question about reflection coefficient

    Hi. I've been trying to understand the phenomenon of step potential, when energy of particle E is higher than the potential V. Then we have solution on both sides of boundary in the form of wave functions... Is the reflection coefficient in this case simply (E-V)/E ?? Can anyone show me a...
  30. T

    QM step potential problem

    Homework Statement Consider particles incident on a one dimensional step function potential, V(x)=Vphi(x) with energy E>V. Calculate the reflection coefficent for particles incident from the right (Barrier height=V at x>0, Barrier height=0 at x<0). Consider the limits as E tends to V and E...
  31. F

    Tunneling through step potential

    Homework Statement Hey, I found this interesting case in the tunneling problem. How do we calculate the transmission probability when the energy of the approaching particle is equal to the height of the potential barrier? I.e E=Vo. Homework Equations Same equations as in other...
  32. C

    Step Potential: Real Physical Situation

    Homework Statement A step potential is defined by: V(x) = 0 ( for for x <0 ) and V(x) = V0 ( for x >0 ). Hence the step occurs at the origin. Suggest a real physical situation, that might correspond to this idealized problem Homework Equations None needed. The Attempt at a Solution...
  33. C

    Solving the Time-Independent Schrödinger Equation for a Step Potential

    Considering a step potential of V(x) = o when x<o and V(x) = Vo when x>o so step occurring at origin of x axis. Write down in words the strategy for solving it. Answer: Solve the time-independent schrodinger equation for V=o when x<o and find the solution for the free particle wave function...
  34. J

    Now we have a step potential

    I am taking a course in solid state electronics at the university and I was thinking about one detail in the calculation of k. In a simple situation like a step potential we say that k=sqrt(2m*abs(E-V))/hbar . Now my question is What happens if the electron approaching the barrier is having an...
  35. I

    Schrodinger's Equation - Step Potential

    In the left side of the barrier, the potential energy V(x)= 0, while on the right side of the barrier, V(x) = V. Given that the total energy of the particle in such a system has a total energy E < V.. a. What are my acceptable solutions? On the left side: Should I include the cos kx...
  36. H

    What Happens When a Particle Encounters a Step Potential Higher Than Its Energy?

    Hi...I've come across this question on a past exam, and I can't seem to resolve it! A particle is incident on a step potential at x=0. The total energy of the particle E, is less then the height of the step, U. The particle has wavefunctions $\begin{array}{l} \psi (x) = \frac{1}{2}\{ (1 +...
  37. G

    Particle Passing Step Potential: A Wave Analysis

    Consider a potential step located at x=0, such that u=0 to the left of the step (for x<0), and u = U to the right of the step (x>0). A particle with total energy E > U traveling from left to right has: \psi_1(x) = Ae^{ik_1x} + Be^{-ik_1x} \;\textrm{for}\; x\le0 \;\textrm{and} \;k_1...
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