# What is Infinite well: Definition and 72 Discussions

In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable.

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1. ### I Momentum eigenfunctions in an infinite well

Hi For an infinite well , solving the Schrodinger equation gives wavefunctions of the form sin(nπx/L). These are not eigenfunctions of the momentum operator which means there are no eigenvalues of the momentum operator. Does this mean momentum cannot be measured ? Inside the infinite well the...
2. ### Stationary states infinite cubic well

For a state to be stationary it must be time independent. Naively, I tried to find the values of c where I don't have any time dependency. ##e^{c \cdot L_z} \psi (r,t) = e^{c L_z} \sqrt{\frac{8}{l^3}} sin(\frac{2 \pi x}{l}) sin(\frac{2 \pi u}{l}) sin(\frac{2 \pi z}{l}) e^{-iEt/\hbar}##...
3. ### Why does a free particle in an infinite well have uncertainty bigger than h/2 ?

So I think I use the right approach and I get uncertainty like this: And it's interval irrelevant(ofc), So what kind of wave function gives us \h_bar / 2 ? I guess a normal curve? if so, why is normal curve could be? if not then what's kind of wave function can reach the lower bound
4. ### A Weyl Fermion in an infinite well

Hello everyone, I have a problem with bounds states of the 1D Weyl equation. I want to solve the Dirac equation ##−i\hbar \partial _x\Psi+m(x)\sigma _z \Psi=E\Psi## with the mass ##m(x)=0,0<x<a##, ##m(x)=\infty,x<0,x>a##. ##\Psi=(\Psi_1,\Psi_2)^T## is a two component spinor. Outside the well...

27. ### Expectation value of energy in infinite well

Homework Statement Given the following normalised time-independent wave function the question asks for the expectation value of the energy of the particle. The well has V(x)=0 for 0<x<a Homework Equations ψ( x ) = √(1/a) ( 1+2cos(∏x/a) )sin(∏x/a) The Attempt at a Solution I...
28. ### Matrix elements of position operator in infinite well basis

Homework Statement Find the eigenfunctions of a particle in a infinite well and express the position operator in the basis of said functions.Homework Equations The Attempt at a Solution Tell me if I'm right so far (the |E> are the eigenkets) X_{ij}= \langle E_i \vert \hat{X} \vert E_j \rangle...
29. ### Uncertainty Principle and the Infinite Well

For the infinite square well in one-dimension the wavefunctions have the form Acos(kx) where k is the wavenumber which is proportional to momentum. Now due to H.U.P. if Δx is fixed as the infinite well size we can't know the exact momentum. I presume this is because the wavefunction exists as a...
30. ### Can someone explain the process of finding c(n) in an infinite well?

we're learning about some of the properties of the steady state wave functions confined in an infinite well. one of the properties was that the steady state wave functions are "complete". and we're learning how to find the coefficient c(n) that "weights" each steady state solution in finding the...
31. ### Estimate energy of infinite well (ground state)

Homework Statement We have to estimate the ground state energy of an infinite potential well (1d) using an argument based on the Heisenberg uncertainty principal. We then are supposed to compare it with the exact value from the eigenvalue equation. Homework Equations Below The...
32. ### Infinite well linear combo of states

Homework Statement A particle of mass m is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2. The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at...
33. ### Infinite Well and Boundary Conditions

Hi All, I would like to know why in the infinite well problem, after having solved the time independent SE, we are not supposed to equal to zero the x derivative of the spatial part of the wave function at -L and L (2L being the total width). We only have to make it zero at the boundary...
34. ### Infinite Well with Schrodinger equation

Homework Statement I'm having a bit of trouble following my textbook, I was under the impression ψ(x) = e^i(kx) = Cos(kx) + iSin(kx) but in my textbook they write the general solution to this equation as ψ(x) = ASin(kx) + BCos(kx). How come they wrote the sin part as not imaginary? isn't this...
35. ### Question About State Collapse and Energy Measurements in Infinite Well

I am just starting out in self-study for quantum theory, so forgive me if my question seems elementary or completely misguided. In quantum mechanics, every wave function ψ can be decomposed into a linear combination of basis functions in the following manner: \Psi = \Sigma{c_{n}\Psi_{n}}...
36. ### Question about an electron confined in an infinite well

Homework Statement An electron confined in an infinite well (1 dimensional) can absorb a photon with a maximum wavelength of 1520 nm, what is the length of the well?Homework Equations λ=2L/n E = hf (photon) E = n^2*h^2/8*m*L^2 The Attempt at a Solution I honestly don't know what to start with...
37. ### Infinite Well with Sinusoidal Potential

Homework Statement Assume a potential of the form V(x)=V_{0}sin({\frac{\pi x}{L}}) with 0<x<L and V(x)=\infty outside this range. Assume \psi = \sum a_{j} \phi_{j}(x), where \phi_{j}(x) are solutions for the infinite square well. Construct the ground state wavefunction using at least 10...
38. ### How Is Photon Energy Calculated When an Electron Moves to a Lower Energy State?

An electron is trapped in an infinite one-dimensional well of width 0.251nm. Initially the electron occupies the n=4 state. Suppose the electron jumps to the ground state with the accompanying emission of a photon. What is the energy of the photon? (Time independent) What I did was...
39. ### Half Infinite Well Homework: Solve for E<0

Homework Statement Homework Equations -h^2/2m d^2F(x)/dx^2 = EF(x) The Attempt at a Solution i just need to a part. for E<0 i can find for 0<x<L side F(x) = ACos(Lx) + BSin(Lx) at the L<x side, F(x) = e^(Kx) where L^2= 2m(E+V)/h^2 K^2= -2mE/h^2 but i do not know what will i do. can...
40. ### Perturbation theory infinite well

in the infinite well with small potential shown in the attachment. I calculated the total energy by using the time independent Schrodinger equation and adding the correction energy to the equation of the slope k=(Vo/L)x. E=h^2/8mL^2 +∫ ψkψ dx ψ=√(2/L) sin⁡(∏/L x) when integrating ∫...
41. ### Perturbation theory infinite well

in the infinite well with small potential shown in the attachment. I calculated the total energy by using the time independent Schrodinger equation and adding the correction energy to the equation of the slope k=(Vo/L)x. E=h^2/8mL^2 +∫ ψkψ dx ψ=√(2/L) sin⁡(∏/L x) when integrating ∫...
42. ### How does potential act as a boundary for electrons in infinite well

Im wondering how potential can act as a boundary for electrons in a 1-D time independent infinite well?
43. ### Barrier in an infinite well

Hello people, I'm trying to plot probability distributions from the given potential numerically. These are the results (particle coming from the right) https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-prn1/s720x720/546478_516459578368236_1799346634_n.jpg What I want to know is why does...
44. ### Electron in a box. Finding the length of the box. (infinite well)

Homework Statement An electron is confined in a one-dimensional box (an infinite well). Two adjacent allowed energies of the electron are 1.068 × 10-18 J and 1.352 × 10-18 J. What is the length of the box? (h = 6.626 × 10-34 J · s, mass of electron = 9.11 × 10-31 kg) Homework Equations \Delta...
45. ### Electron in infinite well equation

Homework Statement An electron is confined in an infinitely deep well of width 0.1nm, about the size of an atom. Estimate the energy of the ground state in eV. Homework Equations Is this the equation I should be using? E=(n^2 hbar^2 ∏^2)/(2m L^2) The Attempt at a Solution
46. ### Infinite well problem, not normal probability function(?)

Homework Statement A particle with mass m is trapped inside the infinite potential well: 0<x<L : U(x) = 0 otherwise: U(x) = ∞ ψ(x,t=0) = Ksin(3∏x/L)cos(∏x/L) What energies can be measured from this system, what are the probabilities for these energies ? Homework Equations Schrödinger...
47. ### Infinite Well Problem - Time Independent Schrodinger's Equation

I'm currently taking a Semiconductor class and we're talking about Schrodinger's Wave Equation, specifically the 1 dimensional time independent form. We were looking at the infinite potential well model: And we divided the graph into 3 different regions: first being the left (or...
48. ### Modern Physics - Length of infinite well that has an electron

Homework Statement ** My book doesn't have any solutions in the back , and I trying to find out if I am doing the problems correctly. My book is Modern Physics for Scientists and Engineers by John C. Morrison. If you know anywhere I can find the Answers. I would greatly appreciate it! The...
49. ### Probabilities Inside Cubic 3D Infinite Well

Homework Statement An electron is trapped in a cubic 3D infinite well. In the states (nx,ny,nz) = (a)(2,1,1), (b)(1,2,1) (c)(1,1,2), what is the probability of finding the electron in the region (0 ≤ x ≤ L, 1/3L ≤ y ≤ 2/3L, 0 ≤ z ≤ L)? Homework Equations My normalized wave function in the...
50. ### How Does an Electron Behave in a One-Sided Infinite Potential Well?

Homework Statement An electron is trapped in a 1D potential described by: V(x) = 0 if x < R0 V(x) = infinity if x > R0 Electron is in lowest energy state, and experiment shows that: (\Delta)x = sqrt(<x2> - <x>2) = 0.181 x 10-10 Show that <x> = 0.5R0 Homework Equations...