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. E

    Probability for finding particle outside potential well

    Homework Statement A particle in the harmonic oscillator potential is in the first excited state. What is the probability of finding this particle in the classically forbidden region? Homework Equations probability of finding particle = integral of abs[psi squared] [a,b] The Attempt...
  2. I

    Classical vs quantum infinite potential well

    Homework Statement This is a problem from Merzbacher. Assuming a particle to be in one of the stationary states of an infinitely high one-dimensional box, calculate the uncertainties in position and momentum, and show that they agree with the Heisenberg uncertainty relation. Also show that...
  3. bknock

    Bizarre results of 1-dimensional delta-function potential well

    I was curious what a delta-function potential barrier would do to a free (E>0) 1-dimensional particle, so I figured it out. I used V = b δ(x) for the potential energy. I got the expected result that full reflection will occur as |b|→∞ or as E→0. These results make sense intuitively when b>0. My...
  4. R

    What is excursion of a potential well?

    What is "excursion" of a potential well? I think it means maximum depth of the well, but I've never heard this term before and I might be wrong. I don't have much of a quantum mechanics background. Details: I'm reading and implementing "Solution of the Schrodinger Equation by a Spectral...
  5. P

    Looking for an analytical solution for a quadratic attractive potential well

    I am trying to derive an equation of motion for a simple electrostatic potential well. Imagine a scenario where an electron (or other charged particle) is released from an arbitrary distance from a fixed (unperturbable) attractive charge (say a proton fixed in space). In 1 dimension, the...
  6. M

    Solve Double Potential Well: Write Equations & Find Wavenumbers

    Homework Statement V(x) = \left\{\infty \textrm{ for } x<0 \left\{0 \textrm{ for } 0<x<a \left\{V_0 \textrm{ for } a<x<a+2b \left\{0 \textrm{ for } a+2bx<2a+2b \left\{\infty \textrm{ for } 2a+2b<x Set up the relevant equations in each region, write down the appropriate solution and...
  7. A

    Finite/Infinite Potential Well Problems

    Hi, (first ever post) I have the following three problems 1) A particle is in the ground state of an infinite well from 0<x<a. Find the probability that it is in the middle half of the well. I think I have managed this, its just the integral of the wave function squared then I put in the...
  8. I

    What Happens to Energy Levels in a Reduced Potential Well?

    if V is reduced to much smaller than the zero point energy then what happens to the ground state and first excited state? for this i know that the function becomes continuous and that the particle is unbound. does this mean that the function will also just have an oscillatory form?
  9. Q

    How Can the Triangular Potential Well TISE Be Simplified?

    Homework Statement Show that the TISE expression you found in part (a): I found it (a) to be: \frac{d^{2} \psi}{dx^{2}} - \frac{2m}{\hbar ^{2}}(e \xi x - E) \psi (x) = 0 Show it (a) can be simplified to: \frac{d^{2} \psi}{dw^{2}} - w \psi = 0 Homework Equations w = z - z0...
  10. K

    How Do You Calculate Energy Levels in a 3-D Infinite Potential Well?

    For the second, third, fourth, and fifth levels of the three-dimensional cubical box, find the energies in terms of the quantity Eo=π2*h2/(2mL2), where m is the particle mass and L is the box's sidelength.
  11. V

    Do All Lower Energy States Exist When n=3 in an Infinite Potential Well?

    ok so i have a question on infinite potential wells... if you have the energy state when n=3, does that mean that you have to have the energy state when n=2 and n=1? Ok basically the Q we are given is: A particle of mass m is trapped in an infi nitely deep one-dimensional potential well...
  12. C

    Two electrons in a potential well

    This question came up in another thread I started about the wave functions of helium vs hydrogen. It's gone off on something of a tangent so I hope I'm not out of line in starting a fresh thread with this topic. I've basically sketched what I would think are the only two realistic candidate...
  13. D

    Rectangular Potential well if hbar -> 0

    Rectangular Potential well if hbar --> 0 Hi, I have a very simple question: My professor said that if \hbar \rightarrow 0 in the transmission coefficient does not yield 0 (case E < V0) as classical results would expect. I think the correct transmission coefficient is solved in Wikipedia...
  14. B

    Basic Infinite Potential Well, Tunnelling, etc.

    I have an exam later today, and I would really apreciate it if someone could check my work or at least point out flaws in my process here. Thanks! Homework Statement At x=0, a proton with a kinetic energy of 10 eV is traveling in the x direction (potential energy = 0). At x=1nm, it...
  15. I_am_learning

    Particle in a potential Well interacts with the wall without touching it?

    Particle in a potential Well interacts with the wall without touching it? The ground state Energy for a particle in an infinite potential well is given by E = h2 / 8mL2 Consider a particle with high mass, say 1 kg. Then the ground state Energy will be very very low. So the velocity of the...
  16. I_am_learning

    Particle In a finite potential well

    For a particle in finite potential well we can have several bound states depending on the height of potential well. Each bound state corresponds to definite energy En. Then corresponding to Each definite Energy there should be definite Momentum Pn. Since we have definite momentum--->...
  17. J

    Finding the Boundary Conditions of a Potential Well

    Homework Statement Show that the conditions for a bound state, Eqn1 and Eqn2, can be obtained by requiring the vanquishing of the denominators in Eqn3 at k=i\kappa. Can you give the argument for why this is not an accident? Homework Equations Eqn1: \alpha=q*tan(qa) Eqn2...
  18. R

    Quantized energy in infinite potential well

    How does energy become quantized in an infinite potential well??
  19. X

    Orthogonality of wave function of finite potential well

    Hello, As we know, the wave function of infinite potential wells form a complete orthogonal base. I have tried now to solve out the wave function for finite potential well, checking the orthogonality, I found that they are no longer orthogonal to each other (I mean the wave function...
  20. A

    Transmission over finite potential well?

    Homework Statement A beam of 500 electrons per second with kinetic energy W1=3eV passes onto potential well (its depth is 5eV and width is 0,3nm). How many electrons per second are transmitted through the well? (It's a poor translation, sorry, but I hope you get the idea of the problem)...
  21. N

    Potential Well Problem: Finding Excited States and Wave Functions

    Homework Statement A particle of mass m moves in one dimension in the following potential well: V(x)=infinity, x<0 , x>L/3 V(x)=0 , 0<x<L/3 a)Circle the general functional form of the 1st excited wave function phi_1(x) in the region 0<x<L/3. k is a positive constant; A is constant as well...
  22. J

    Width of Finite Potential Well

    For an electron in a certain rectangular well with a depth of 20.0 eV, the lowest energy level lies 3.00 eV above the bottom of the well. Find the width of this well. Hint: Use tan theta = sin theta/cos theta. Equation for energy levels in a rectangular well...
  23. O

    How Does the Infinite Potential Well Illustrate the Uncertainty Principle?

    infinite potential well and the uncertainty principle the solution for Schroedinger equation in infinite potential well satisfy the following energy levels: where l is the width of the well. E can't be zero since then \psi=0 so there isn't any particle in the well . i read in...
  24. E

    What is the true nature of vacuum energy in quantum physics?

    Hi! Let's suppose an electron in a mono-dimensional potential well. According to Heisenberg uncertainty principle, if L is the length of the well, then I have a momentum greater than \frac{h}{L}, which means that the electron has a velocity (and so a kinetic energy) greater than \frac{h}{L*m_e}...
  25. M

    Particle in an infinite potential well

    Homework Statement The nth energy level for a particle of mass m confined in an infinite potential well is given by: where L is the width of the well and h is Planck’s constant. Assuming that the uncertainty in the particle’s momentum is equal to the momentum itself, show that the...
  26. D

    Changing The Shape of a potential well

    This question was posed to me a while ago, but I never fully understood how to solve it. You have a particle in the first excited state of the infinite square well (with the origin taken to be at the center. You "abruptly" change the shape of the potential well to be that of the harmonic...
  27. A

    Quantum mechanics potential well solutions-help

    I was working through the textbook and it just gave the solutions to the potential well barrier as in [B/A]*2 and [F/A]*2 and T i was trying to figure it out with the conditions but couldn't get the answer i have attached the conditions, can some one show me how to find these values from the...
  28. D

    Finite Spherical Potential Well

    This is more a qualitative question than a specific homework question, but a homework problem got me wondering about it. I was solving the finite potential well. V(r) = 0 \hspace{1cm} r \geq a V(r) = -V_0\hspace{1cm} r < a I am trying to solve for the ground state energy. When I find...
  29. H

    Dirac Equation for a moving square potential well

    Hi, I have learned the Dirac equation recently and I managed to solve it for a free particle (following Greiner book “relativistic quantum mechanics” and Paul Strange book “Relativistic Quantum Mechanics”). I was asked to solve the Dirac equation in the stationary frame for a free particle (no...
  30. B

    Infinite potential well with V(x)=Asin(x pi/a)

    Homework Statement Hi, this is basically a particle in a box problem but V(x) is sinusoidal inside the box. V(x)=-Asin(pi x/a) 0<x<a V(x)=Infinity otherwise A: depth of the well In the question, it asks me to plot the first 4 eigenfunctions. The Attempt at a...
  31. V

    Infinite potential well and linear superposition

    Homework Statement Consider a particle in a potential ; V(x)=0\ for\ 0<=x<=L and V(x)=\infty\ otherwise . Its wave function is a linear superposition of the lowest two stationary states and given by \psi(x,t)=\frac{1}{2}*(\sqrt{3}...
  32. T

    Quantum Mechanics - Infinite Potential Well

    Homework Statement A particle is trapped in an infinite potential well, with the infinite walls at ±a. At time t=0, the wavefunction of the particle is \psi = \frac{1}{\sqrt{2a}} between -a and a, and 0 otherwise. Find the probability that the Energy of the particle is \frac{9...
  33. B

    Identical bosons vs. fermions in square potential well

    The following Wolfram web page shows the probability density functions for two identical bosons in a square potential well. It also shows the probability density for two identical fermions. http://demonstrations.wolfram.com/WaveFunctionsOfIdenticalParticles/ So it appears that each is...
  34. D

    Complexity of Solving Multi-Potential Schrodinger Equation?

    Homework Statement Does anyone now how to solve the schrodinger equation for a potenital such that: V1(0<x<a), v2(a<x<b), v3(b<x<c). Also i need to write down the condition which gives the possible energy eigenvalues of a particle in the potential. ITs easily to solve the first potential well...
  35. E

    Does an Infinite Potential Well Have a Box in the Middle?

    Homework Statement An infinite potential well with a box in the middle V = 100, the walls of the box go from -L/2 to L/2. Homework Equations Schrodinger's equation. The Attempt at a Solution Please help.
  36. S

    Electron In An Infinite Potential Well

    Homework Statement An electron is in a Infinite potential well (1-dimensional box with infinite wall boundary conditions) at the second energy level. The width of the box is L. What is the electron density n(x) as a function of the position x? Homework Equations time-independent Schrödinger...
  37. S

    Radial function in Spherical potential well

    Homework Statement A Spherical potential which is 0 for 0<r<a Vo for r>a Find the condition for bound states, for the radial function with l=0 Plot the result.The Attempt at a Solution I have gotten the equation - tan(ka)=k/lambda where k is the wavenumber for the wave inside the well and...
  38. P

    Calculate the energy levels for a generalized potential

    Hi, I need to calculate the energy levels for a generalised potential, which forms a double well, on Matlab as part of a project but I need to understand it analytically first. There doesn't seem to be much information about the topic on the web or in books I checked. I read the following...
  39. Y

    Asymmetric potential well problem

    The task is to find a wavefunction (doesn't need to be normalised) and the energy levels of a particle in an asymmetric potential well (a Schrodinger problem). i.e V = V1 for x<0, 0 for 0<x<d and V = V2 for x>d. What I've got so far is Let α^2= 2m (E-V1)/ℏ^2 β^2= 2mE/ℏ^2...
  40. N

    Infinite vs Finite potential well

    Hi, I have learned about the infinite quantum well last week and today the finite quantum well was introduced. There is however one thing I don't completely understand, or which I'm not completely happy with. In the case of the finite well, the shrodinger equation is solved for both inside...
  41. A

    Electron in potential well equation

    Hφ(x) =((p2op)/2m + V(x))φ(x) = (-hbar2/2m.d2/dx2+ V(x)φ(x) = E φ(x) This equation is supposed to relate to an electron confined in a one-dimensional potential well. I'm really confused about where it comes from and I do not know what V(x) represents. If anyone could help explain this...
  42. F

    Solve Delta Potential Well for Scattering Matrix & Prove Unitarity

    Homework Statement consider the scattering matrix for the potential 2m/hbar2 V(x) = λ/a δ(x-b) show that it has the form (2ika/(2ika-λ) , (e-2kib) λ/(2ika-λ) (e2kib) λ/(2ika-λ) , 2ika/(2ika-λ) (I've used commas just to separate terms in the matrix) prove...
  43. S

    Wavefunction: Particle in a 1-dimensional potential Well

    Homework Statement Find the wave function of particle in a 1-dimensional potential Well of length L, n=2 and mass m Homework Equations I think this would be the wave equation, but not 100% sure [tex]\varphi=Asin(n\pix/L)[\tex] where n=1,2,3... tex doesn't work for me---=Asin[n*pi/L] The...
  44. B

    Evaluate QM Potential Well Proposal for Low-n Transitions

    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 (an electron trapped in a one dimensional box made of electrodes and grids in an evacuated tube)...
  45. B

    Quantum mechanics: 1D potential well instananeously expanded to twice its size

    Homework Statement Consider a particle confined in a 1D potential well of length L. Derive the normalized wavefunctions and energies of the eigenstates of the system in terms of the quantum number n, working from the time independent Schördinger equation. With the particle initially in the...
  46. S

    Why Does a Wave Packet Better Describe a Particle in Quantum Mechanics?

    1.in the attached file see the fig 8.5 What is the the physical reason,for which ahe amplitude of the wave function is larger in between x=0 & x= a ? 2.what is the reason for choosing a wave packet to describe a particle ?
  47. D

    An Electron and Neutron in a Finite Potential Well

    Problem Given that \frac{2ma^2 |V|}{\hbar^2} = \left(\frac{7\pi}{4}\right)^2 for an electron in a potential well of depth |V| and width 2a = 10^{-7} \text{cm}, if a 100\text{-keV} neutron is scattered by such a system, calculate the possible decrements in energy that the neutron may...
  48. J

    What is the purpose of using a potential well to model a particle's confinement?

    What does a particle in a potential well means? What is the physical interpretation of it? Could anyone anser this topic
  49. E

    How Does Particle Energy Affect Transmission Probability in a Potential Well?

    If you think this will get more replies in the intro phys please let me know and i will move it: A particle of total energy 9Vo is incident from the -x axis on a potential given by: V \left\{8Vo, x<0\right\} \left\{0, 0<x<a\right\} \left\{5Vo, x>a\right\} Find the probability that the...
  50. P

    Energy levels in a potential well

    I know this question seems very simple which is why its bugging me so much: Why is the ground state energy not zero? A simple answer would be greatly appreciated
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