What is Potential well: Definition and 231 Discussions

A potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy (kinetic energy in the case of a gravitational potential well) because it is captured in the local minimum of a potential well. Therefore, a body may not proceed to the global minimum of potential energy, as it would naturally tend to due to entropy.

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  1. B

    Linearly Increasing Potential Well. Help

    [Note: no template because this post was moved from the QM subforum] I was working on problem #41 and was confused about what the wave function would look like from the time x = 0 to when E=V0. (See image in...
  2. B

    Energy units in the potential well problem

    Homework Statement (Please look at the attached file too) In one dimension time independent potential well, I want to know what is a suitable unit for energy (electron volts or joule) Homework Equations The Attempt at a Solution In the attached picture, I've tried to analyze each...
  3. R

    First-order perturbation for a simple harmonic potential well

    Homework Statement The ground state of the wavefunction for an electron in a simple one-dimensional harmonic potential well is \Psi _{0}(x)= \left ( \frac{m\omega }{\pi \hbar} \right )^{1/4} exp(-\frac{m\omega x^{2}}{2\hbar}) By employing first-order perturbation theory calculate the energy...
  4. A

    What Are the Eigenfunctions for the 1D Infinite Square Well?

    Homework Statement Find the ground and first excited state eigenfunctions of for the 1D infinite square well with boundaries -L/2 and +L/2 Homework Equations $$\frac{-\hbar^2}{2m}\frac{\partial^2}{\partial x^2}\psi(x) = E\psi(x)$$ The Attempt at a Solution Okay so I know how to solve it and...
  5. B

    Why does infinite potential well give rise to standing wave?

    For a particle in a box that is described with a wave function, why can there only be a standing wave when there is an infinite potential well? From my understanding, the infinite potential well makes it impossible for the particle to tunnel through the barrier and so the wave function cannot...
  6. feynwomann

    Solve Finite Potential Well: Schrödinger Eqn. & k=qtan(q*a)

    ' I've got these solutions to the Schrödinger equation (##-\frac{\hbar} {2m} \frac {d^2} {dx^2} \psi(x) + V(x)*\psi(x)=E*\psi(x)##): x < -a: ##\psi(x)=C_1*e^(k*x)## -a < x < a: ##\psi(x)=A*cos(q*x)+B*sin(q*x)## x > a: ##\psi(x)=C_2*e^(-k*x)## ##q^2=\frac {2m(E+V_0)} {\hbar^2}## and ##k^2=\frac...
  7. F

    Electron in a One Dimensional Infinite Potential Well

    Homework Statement An electron is confined to a narrow evacuated tube. The tube, which has length of 2m functions as a one dimensional infinite potential well. A: What is the energy difference between the electrons ground state and the first excitied state. B: What quantum number n would the...
  8. 2

    Variance in position for the infinite square potential well?

    [Note from mentor: this thread originated in a non-homework forum, therefore it doesn't use the standard homework template] ------------------------------------------ This exercise pops up in the Cavendish Quantum Mechanics Primer (M. Warner and A. Cheung) but I can't seem to figure it out. So...
  9. J

    One dimensional potential well

    Homework Statement A particle of mass m is confined in a one dimensional well by a potential V. The energy eigenvalues are E_{n}=\frac{\hbar^2n^2\pi^2}{2mL^2} and the corresponding normalized eigenstates are \Phi_{n}=\sqrt{\frac{2}{L}}sin(\frac{n\pi x}{L}) At time t=0 the particle is in the...
  10. I

    How Does a Particle Behave in a 2-Level Finite Potential Well?

    Consider a particle of mass m subject to the following potential function (taking Vo and L to be positive): V (x) = 40 Vo if x < 0; 0 if 0 < x < L/2; 2 Vo if L/2 < x < L; 40 Vo if x > L. (a) Derive the transcendental equation for energy eigenstates having an energy 2 Vo < E < 40 Vo. To simplify...
  11. W

    Explore Formation of Bound State in a Delta-Function Potential Well

    Homework Statement We learned in class that a particle exposed to a 1D delta-function potential well would always have a single bound state. Let us now explore this question for the case where the delta-function potential well is situated in the vicinity of the impenetrable potential wall...
  12. D

    Quantum Physics - Electron in a 1d Potential Well Question

    Homework Statement This is a Quantum Physics problem. An electron moves in a one-dimensional potential well such that the potential V = 0 for |x| ≤ a, and V = ∞ otherwise. The system has energy eigenfunctions: Un = a^(-1/2) cos (n∏x/2a), for n odd, and Un = a^(-1/2) sin (n∏x/2a)...
  13. R

    Spin assumption for fermions in potential well.

    Hi, Assume I’m solving a 2-particle (fermions) problem in a potential well. If I set the wavefunction as anti-symmetric, then by default I’m assuming that the two particles has the same spin and hence exchange interaction has to be accommodated for. But what if the 2 fermions have different...
  14. M

    What Could Be Wrong with My Calculations in the Infinite Potential Well Problem?

    three parts to this one, I can't seem to justify my values, units cancel, but the numbers don't seem right. I think I may have used a wrong equation for part B but I don't know what else to use. Problem: An electron is confined to an infinitely deep potential well of width 0.120 nm. a.)...
  15. U

    Particle in infinite potential well

    Homework Statement Sketch the difference of probability distributions at the two times. Does the energy change with time? The potential well suddenly disappears, what is the form of the wavefunction? Homework Equations The Attempt at a Solution Part (a) At t = 0, the probability...
  16. B

    What happens to psi in Infinite potential well

    What happens to ψ in a infinite potential well when the width is suddenly reduced to half its previous value ? Will this instantly adjust ψ to the new size of the well or will it take some time to confine itself in this new well ? And is there a possibility of quantum tunneling here?
  17. U

    Cosine perturbation to potential well

    Homework Statement Part (b): Find the perturbed energy. Homework Equations The Attempt at a Solution I've solved everything, except part (b). I got an answer of 0 for part (b) for all orders, which is kind of strange, as one would expect some perturbation. \Delta E_n = \langle \psi_n...
  18. U

    Is the wavefunction for this system unique?

    Homework Statement Part (a): Find wavefunction and energy levels. Part (b): Find a possible wavefunction. Is this wavefunction unique? Part (c): What is the probability of finding it in the ground state? Part (d): What's the probability of finding it in the second excited state? Homework...
  19. U

    Sudden Perturbation of Potential Well

    Homework Statement Part (a): Particle originally sits in well V(x) = 0 for 0 < x < a, V = ∞ elsewhere. The well suddenly doubles in length to 2a. What's the probability of the particle staying in its ground state? Part (b): What is the duration of time that the change occur, for the...
  20. 4

    Infinite potential well proposal

    Infinite potential well "proposal" Homework Statement An experimental physicist submits a proposal to a granting agency requesting support to construct an infinite potential well analogous to the one shown in Figure 3.5. Specifically, the proposal is to build a well with L = 1mm, inject some...
  21. L

    Acceleration. Infinite potential well.

    Why we don't have acceleration in quantum mechanics. For example why particle in infinite potential well can not accelerate. For example dimension of well is ##L## and ##L=\frac{at^2}{2}##, where ##a## is acceleration.
  22. S

    Hydrogen atom: potential well and orbit radii

    Hello, I happened to open up an old book by Sah, and in it he says: "it is evident that the electron orbit radius is half the well radius at the energy level E_n" The orbit radius is r_n=\frac{4*\pi*ε_0*\hbar^2*n^2}{mq^2} and the potential well...
  23. Ace10

    Infinite potential well with Delta function inside

    Hello guys, I need some serious help for the solution of a problem in Q.M, I'm not so sure if I deal with it properly.. Consider an infinite potential well with the traits: V(x):∞, for x>a and x<-a...
  24. W

    Characteristics of a Potential Well that is Proportional to -1/|x|

    Regarding a potential well that is proportional to -1/|x|, are the amount of possible energy levels finite or infinite? (The potential well is narrow in the middle and approaches a horizontal asymptote as you leave the middle, like the shape of a tornado). I figured it would be infinite...
  25. W

    A particle in 1D potential well

    Hello, What does it means when a particle having mass "m" in a one dimensional potential well has the potential given by: V(x)= \stackrel{-\alpha δ(x) for |x|<a}{∞ for |x|≥a} where δ(x) is the delta function and \alpha is a constant. I understand that the well boundries have...
  26. skate_nerd

    Potential well, harmonic oscillator

    Homework Statement Parabolic harmonic oscillator potential well. A particle is trapped in the well, oscillating classically back and forth between x=b and x=-b. The potential jumps from Vo to zero at x=a and x=-a. The particle's energy is Vo/2. I need to find the potential function V(x) in...
  27. R

    I really need a resource to explain the linear potential well to me

    So I am trying to learn this. It is not making sense to me. Every single resource I have found tells me I need to make some weird substitution, and then it becomes a differential equation that has the Airy equation as a solution, and then skips to finding the energy eigenvalues as a function of...
  28. C

    Understanding the Role of Gamma in the Semi-Infinite Potential Well Problem

    Homework Statement Let V(x) = +∞ for x ≤ 0, -V1 for 0 < x < b and 0 for x > b. V1 and b are positive. The solutions in each of the physical regions are ##\psi_1 = P \exp(ik_1 x) + Q \exp (-ik_1 x)## and ##\psi_2 = R \sin (k_2x + \gamma)##. Show that ##\lim_{V_1 \rightarrow 0} \gamma = 0##...
  29. V

    Concepts about infinite potential well

    As we know, the 1d infinite potential well has a stationary state. The function that depends on x onky is a sin function. However, I don't understand the concept in this question. I have the answer of this question and this is not a homework. I am not asking for the answer so please don't put...
  30. P

    A question about Dirac Delta Potential Well solution

    In Griffith's Introduction to Quantum Mechanics, on page 56, he says that for scattering states (E > 0), the general solution for the Dirac delta potential function V(x) = -aδ(x) (once plugged into the Schrodinger Equation), is the following: ψ(x) = Ae^(ikx) + Be^(-ikx), where k = (√2mE)/h...
  31. 7

    Particle in a potential well - not infinite :/

    Homework Statement Homework Equations Stationary Schrodinger equation. The Attempt at a Solution 1st I draw the image of the well, so we can talk better - otherwise this makes no sense as it looks like a complex homework. In the image ##W_p## marks the potential energy but never mind i ll...
  32. A

    Quantum physics potential well.

    Homework Statement In the instant t=0, we have the following wave function of a particle in a infinite potential well with a width a. \psi (x) = \sqrt{\frac{2}{a}}\text{Sin}\left[\frac{n*\text{Pi}*x}{a}\right] Calculate the momentum space wave function. Ok, i just want to...
  33. Roodles01

    Particle in a potential well of harmonic oscillator

    Homework Statement I have a similar problem to this one on Physicsforum from a few years ago. Homework Equations Cleggy has finished part a) saying he gets the answer as Ψ(x, t) = (1/√2) (ψ1(x)exp(-3iwt/2+ iψ3(x)exp(-7iwt/2) OK classical angular frequency ω0 = √C/m for period of...
  34. I

    Resonance in a damped triangular potential well

    I have a potential well which is an infinite wall for x<0 and a linear slope for x>0. There is damping proportional to velocity. Basically, it's a ball bouncing elastically off the ground and with air friction included. I wonder if there is some periodic driving force which will cause one...
  35. Rorshach

    Infinite potential well with a step

    Homework Statement Hey guys:) Maybe you will be able to help me with this problem i got as an assignment for my quantum mechanics course, it goes as follows: a particle of mass m moves in the potential for x<0 infinity, for 0<x<a -U, for a<x<b 0, for b<x infinity. a) Sketch the...
  36. 7

    Energies and numbers of bound states in finite potential well

    Hello I understand how to approach finite potential well. However i am disturbed by equation which describes number of states ##N## for a finite potential well (##d## is a width of a well and ##W_p## is potential): $$ N \approx \dfrac{\sqrt{2m W_p}d}{\hbar \pi} $$ I am sure it has something to...
  37. 7

    Plotting a wavefunction for a finite potential well doesn't work out

    Lets say we have a finite square potential well like below: This well has a ##\psi## which we can combine with ##\psi_I##, ##\psi_{II}## and ##\psi_{III}##. I have been playing around and got expressions for them, but they are not the same for ODD and EVEN solutions but let's do this only...
  38. E

    Understanding SHM in a Potential Well: F(x+xo) and dU/dx Link Explained

    In the attachment below some form of link is made between F(x+xo) and dU/dx I understand F=-dU/dx but I do not understand the derivation shown to prove that the force constant is equal to the second derivative in the last line. How do they go about this proof ?
  39. B

    Double Delta function potential well

    Consider a one-dimensional system described by a particle of mass m in the presence of a pair of delta function wells of strength Wo > 0 located at x = L, i.e. V(x) = -Wo (x + L) - Wo(x - L) This is a rough but illuminating toy model of an electron in the presence of two positive. charges...
  40. 7

    Finite Potential Well Solutions

    Lets say we have a finite square well symetric around ##y## axis (picture below). I know how and why general solutions to the second order ODE (stationary Schrödinger equation) are as follows for the regions I, II and III. \begin{align} \text{I:}& & \psi_{\text{I}}&= Ae^{\kappa x} \\...
  41. L

    Translation operator. Infinite potential well.

    For potential well problem for well with potential which is zero in the interval ##[0,a]## and infinite outside we get ##\psi_n(x)=\sqrt{\frac{2}{a}}\sin \frac{n\pi x}{a}##. If I want to get this result for well with potential which is zero in the interval ##[-\frac{a}{2},\frac{a}{2}]## and...
  42. C

    Question about potential well schrodinger

    So been self-studying till this point and it has been pretty easy / generic with the PDE's. At this point though the math gets a bit more out of my depth and was curious if someone might lend a hand in helping me understand what is going on. My question is pretty much is there a good algorithm...
  43. M

    What is the condition for one-dimensional motion in an infinite potential well?

    In one dimensional problem of infinite square potential well wave function is ##\phi_n(x)=\sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L}## and energy is ##E_n=\frac{n^2\pi^2\hbar^2}{2mL^2}##. Questions: What condition implies that motion is one dimensional. Did wave function describes motion of...
  44. A

    Electron in a potential well (numerical problem)

    Homework Statement The width of the potential well of an electron can be assumed to be 2angstrom. Calculate the energy of an electron (in joules and eV) from this information for various values of n. I believe I have messed up my units somewhere in the final calculation, but I have...
  45. bcrowell

    What is the behavior of an electron in an asymmetric potential well?

    Consider a nonrelativistic electron in one dimension, with the potential V(x)=\left\{ \begin{matrix} \infty, \quad x<-a \\ -4V_0, \quad -a<x<0 \\ -V_0, \quad 0<x<a \\ \infty, \quad x>a \end{matrix} \right. I use this as an example when I teach the Schrodinger equation in a...
  46. T

    Eigenvalues and Eigenfunctions for a Delta Potential Well

    Homework Statement Consider this situation, V(x)=λδ(x) ,-a<x<a. V(x)=∞,x>a or x<-a. How to find the eigenvalue and eigen wavefuntion of the Hamiltonian. Homework Equations i can only reder to stationary Schrodinger equation. The Attempt at a Solution when it is ouside the well(x>a...
  47. J

    Potential Well - a theoretical question

    So imangine a potential well that looks like this: --_-- where the 1st and the third line have a potential U and the 2nd line has U=0. A wavefunction is coming from the left with E>U. When the wave function hits the first potential change(where the ΔU = negative), does some of the...
  48. S

    Electron Wavelength in Infinite Potential Well

    I'm a little confused about the electron wavelength in an infinite potential well. It is my understanding that the maximum wavelength that the electron can achieve is 2 times the length of the potential well. As the eigenvalue increases, does the wavelength change? I believe that the...
  49. W

    Electromagnetic potential well, impossible?

    I was having a discussion with my friend the other day. He had just attended a lecture about Paul traps. He told me that the Paul trap potential has a stationary point in the middle, which is a saddle point, and that the 2 pairs of opposite poles are oscillating between being positive and...
  50. G

    Sphereically Symmetric potential well

    Homework Statement A particle that movies in three dimensions is trapped in a deep spherically symmetric potential V(r): V(r) = 0 at r < r_{}0 --> ∞ at r ≥ r_{}0 where r_{}0 is a positive constant. The ground state wave function is spherically symmetric, so the radial wave function u(r)...
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