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...
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}##...
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
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...
(a) I guess I should find ##C_n## by normalizing ##\psi_n##.
$$∫_{∞}^∞|C_nψn(x)|^2 dx=C_n^2 \frac{2}{a}∫_0^a sin^2(\frac{πnx}{a})dx=1$$
$$C_n^2 \frac{2}{a}[\frac{a}{2}−\frac{a}{4πn}sin(\frac{2πna}{a})]=1⇒C_n=1$$
(b) $$Hψ_n(x)=\frac{-ħ^2}{2m}\frac{\partial^2}{\partial...
As the temperature given was 0K, I calculated the ground state energy of the system. I considered 2 electrons to be in the n=1 state, 2 in the n=2 state and 1 in the n=3 state by Pauli's exclusion principle.
By this configuration, I got the total energy of the system in the ground state to be...
Hello, I am trying to find the solution of Schrödinger equation on matlab. However, when I apply boundary conditions, MATLAB only gives me the solution with both coefficients 0. I want to find the solution : Asin(n*pi*x/L)
You can see my code below. Could you please tell me where is my mistake...
I am currently stuck trying to work this out. I have an infinite potential with walls at x=0 and x=a, with the initial state:
$$
\psi(x,0) = A_2(exp(i\pi(x-a)/a)-1)
$$
I am trying to find psi(x,t). I know that
$$
A_2(exp(i\pi(x-a)/a)-1) = A_2(-exp(i\pi/a)-1)
$$
And this enables me to find...
We have a 1 dimensional infinite well (from x=0 to x=L) and the time dependent solution to the wavefunction is the product of the energy eigenstate multiplied by the complex exponential:
\Psi_n(x, t) = \sqrt{\frac{2}{L}} \sin(\frac{n\pi x}{L}) e^{-\frac{iE_n}{\hbar}}
Now, I want to create a...
In Zettili's Quantum Mechanics, page 477, he wants to determine the energy and wave function of the ground state of three non-interacting identical spin 1/2 particles confined in a one-dimensional infinite potential well of length a. He states that one possible configuration of the ground state...
Homework Statement
First sorry for the traduction mistakes.
Prove that any wave function of a particle in a 1 dimensional infinite double well of width a, returns to its original state in time T=4ma2/(πħ) .
Homework Equations
Ψ(x,t)=∑cnψn(x)·exp(-i·Ent/(ħ))
En=n2π2ħ2/(2ma2)
The Attempt at a...
I'm trying to get the eigenfunctions and eigenvalues (energies) of an infinite well in Python, but I have a few things I can't seem to fix or don't understand...
Here's the code I have:
from numpy import *
from numpy.linalg import eigh
import matplotlib.pyplot as plt
from __future__ import...
It is required to be continuous in the following text:
The book's reason why wave functions are continuous (for finite V) is as follows. But for infinite V, ##\frac{\partial P}{\partial t}=\infty-\infty=## undefined, and so the reason that wave functions must be continuous is invalid...
Homework Statement
This is problem 17 from Chapter 3 of Quantum Physics by S. Gasiorowicz
"Consider the eigenfunctions for a box with sides at x = +/- a. Without working out the integral, prove that the expectation value of the quantity
x^2 p^3 + 3 x p^3 x + p^3 x^2
vanishes for all the...
Homework Statement
Determine what colors of visible light would be absorbed by electrons in an infinite well, N = 3.1 nm. The effective mass for an electron is one-fifteenth of the standard electron mass.
Homework Equations
En = n2h2/(8mL2)
E = hf
f = c/λ
The Attempt at a Solution
E1 =...
I apologize in advance for not being familiar with LaTex.
1. Homework Statement
One thousand neutrons are in an infinite square well, with walls x=0 and x=L. The state of the particle at t=0 is :
ψ(x,0)=Ax(x-L)
How many particles are in the interval (0,L/2) at t=3?
How many particles have...
Homework Statement
For the particle in a box given in the above question, what is the probability of finding the electron between (i) x = 0.49 and 0.51, (ii) x = 0 and 0.020 and (ii) x=0.24 and 0.26 ( x in nm) for both n=1 and n=2. Rationalize your answers.
Homework Equations...
Homework Statement
An electron is bound in a square well of depthU0=6E1−IDW.
What is the width of the well if its ground-state energy is 2.50 eV ?
Homework Equations
En = h2n2/8mL2
The Attempt at a Solution
I used n = 1
so I get:
25eV*1.6*10-19 = h2/8*9.11*10-31*L2
I got L = .388 nm. It...
For time independent Schrodinger's equation in 3-D
Where Enx,ny,nz=(nx/Lx2+ny/Ly2+nz/Lz2)(π2ħ2/2m
and Ψnx,ny,nz=Asin(nxπx/Lx)sin(nyπy/Ly)sin(nzπz/Lz)
How do I normalize A to get (2/L)^3/2?
I don't think I understand how to normalize constants.
Hi everyone,
I need help for preparing a Hamiltonian matrix.
What will be the elements of the hamiltonian matrix of the following Schrodinger equation (for two electrons in a 1D infinite well):
-\frac{ħ^{2}}{2m}(\frac{d^{2}ψ(x_1,x_2)}{dx_1^{2}}+\frac{d^{2}ψ(x_1,x_2)}{dx_2^{2}}) +...
Homework Statement
I Have tried to solve a problem about infinite potential well with a delta well in the middle, but I haven't the results and so I can't check if the proceeding is wrong. I post the steps that I have followed hoping someone can help me to understand.
We have a particle in 1D...
Homework Statement
The bottom of an infinite well is changed to have the shape
$$V(x) = \epsilon \sin {\dfrac{\pi x}{b}}, 0 \le x \le b$$
Calculate the energy shifts for all the excited states to first order in ##\epsilon##. Note that the well originally had ##V(x) = 0## for ##0 \le x \le...
Hi there
I am trying to find bound state energies assuming infinite potential. I have been told it can be done by analytically solving Right Hand Side and Left Hand Side of an equation such as:
E^1/2 tan(2ma^2E/4hbar)^1/2 = (V0-E)^1/2
If solved properly, it should give one curve (RHS), crossed...
Homework Statement
The potential for a particle mass m moving in one dimension is:
V(x) = infinity for x < 0
= 0 for 0< x <L
= V for L< x <2L
= infinity for x > 2L
Assume the energy of the particle is in the range 0 < E < V
Find the energy eigenfunctions and the equation...
Homework Statement
http://puu.sh/bTtVx/ba89b717b8.png
Homework Equations
I've tried using the integral method of Schrodinger's eq, getting:
(X/L - (1/4pi)sin(4xpi/L) from x1 to x2.
The Attempt at a Solution
I've tried plugging in the values of x given in the problem to the above equation...
Homework Statement
A particle of mass ##m## is constrained to move between two concentric hard spheres of radii ##r = a## and ##r = b##. There is no potential between the spheres. Find the ground state energy and wave function.
Homework Equations
$$\frac{-\hbar^2}{2m} \frac{d^2 u}{dr^2} +...
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...
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...
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...
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...
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...
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...
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...
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...
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}}...
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...
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...
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...
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...
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 ∫...
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 ∫...
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...
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...
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
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...
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...
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...
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...
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...