In quantum mechanics, the rectangular (or, at times, square) potential barrier is a standard one-dimensional problem that demonstrates the phenomena of wave-mechanical tunneling (also called "quantum tunneling") and wave-mechanical reflection. The problem consists of solving the one-dimensional time-independent Schrödinger equation for a particle encountering a rectangular potential energy barrier. It is usually assumed, as here, that a free particle impinges on the barrier from the left.
Although classically a particle behaving as a point mass would be reflected if its energy is less than
V
0
{\displaystyle V_{0}}
, a particle actually behaving as a matter wave has a non-zero probability of penetrating the barrier and continuing its travel as a wave on the other side. In classical wave-physics, this effect is known as evanescent wave coupling. The likelihood that the particle will pass through the barrier is given by the transmission coefficient, whereas the likelihood that it is reflected is given by the reflection coefficient. Schrödinger's wave-equation allows these coefficients to be calculated.
Homework Statement
The well is set up exactly like this https://www.physicsforums.com/showthread.php?t=397977&highlight=potential+barrier+inside+an+infinite+square+well. It is basically a infinite potential well with a barrier in the center.
Basically I've got solutions for regions 1, 2...
Homework Statement
In delta potential barrier problem Schrodinger equation we get
\psi(x)=Ae^{kx}, x<0
\psi(x)=Ae^{-kx}, x>0
We must get solution of
lim_{\epsilon \rightarrow 0} \int^{\epsilon}_{-\epsilon}\frac{d^2\psi}{dx^2}dx
Homework Equations
The Attempt at a Solution
lim_{\epsilon...
Electron beam with kinetic energy E_{k} = 10 eV strikes a positive potential barrier V_{0} and the kinetic energy after the beam has passed through the barrier is E_{k} = (10 eV -V_{0}).
How big potential V_{0} is needed so that 40% of the electron beam is going to be reflected?
What...
Homework Statement
A beam of particles, each of mass m and kinetic energy E, is incident on a potential barrier
V(x) = V_0 \; \; for \; \; 0 \leq x \leq a
\; \; \; \; \; \; \; \; \; = 0 \; \; for \; \; x < 0 \; \; and \; \; x > a
E = V_0 \; \mbox{is the special case}
The part...
Electron beam with kinetic energy E_{k} = 10 eV strikes a positive potential barrier V_{0} and the kinetic energy after the beam has passed through the barrier is E_{k} = (10 eV -V_{0}).
How big potential V_{0} is needed so that 40% of the electron beam is going to be reflected?
What...
Homework Statement
In a particular atom, an alpha particle makes N collisions with a potential barrier in each second. The transmission coefficient at the barrier is 1.0e-15. In one second, 2.0e18 alpha particles are emitted from a group of 3.0e23 radioactive atoms.
Find N.
Homework...
Barrier potential, E> V0
V(X) = 0 ( x < 0 )
= V0 ( 0 < x < a )
= 0 ( x> a )
Psi(x)1 = Aexp[ik1x] + B exp[-ik1x]
Psi(x)2 = Cexp[ik2x] + D exp[-ik2x]
Psi(x)3 = Fexp[ik1x] + G exp[-ik1x] ( K3= K1 so I put k1 )
and G = 0 because there is no reflection,
I used B.C...
If you have a rectangular square potential barrier of some height, say \lambda/L, and thickness L, what is the transmission coefficient and what is its value in the limit that L goes to 0?
Thus you have the height of the barrier going to infinity, while the width goes to zero... Assuming...
Homework Statement
To calculate the height of the potential barrier for a head on collision between two deuterons given that each deuteron is a sphere of radius R
Homework Equations
Potential of the first deuteron at a distance of 2R from it =V = ke/2R where k = 9 * 10^9 ,
e= 1.6 *...
Homework Statement
I am trying to find the coefficients in a Schrodinger equation approaching a finite potential.
https://www.physicsforums.com/showthread.php?t=203385
It is a problem similar to this, except a little easier. In my case, though, there is no V1 as shown in the picture at the...
HI,all
This is rajasekhar ,
Please guide me how to solve below problem.
An electron moves in a one-dimensional potential of width 8 angstroms and depth 12eV then how to found number of bound states present?
Thanks&Regaurds
HI,all
This is rajasekhar ,
Please guide me how to solve below problem.
An electron moves in a one-dimensional potential of width 8 angstroms and depth 12eV then how to found number of bound states present?
Thanks&Regaurds
Homework Statement
Consider the diagram described by: http://filer.case.edu/pal25/well.jpg
If a particle with E = \frac{-\hbar^2 q^2}{2m} comes in from negative infinity with amplitude 1, what is the wave function for negative x?
Oh and V(x) < -a and > a = 0
Homework Equations...
Homework Statement
An electron approaches a potential barrier 10 eV high and 0.5 nm wide. If the electron has a
1% chance of tunnelling through, what must be its energy?
Homework Equations
don't know how to put equations in eg how do i get something like alpha and theta etc...
Homework Statement
write the solutions to the S.E in regions x<o and x between o and a
C:\Users\karthik\Desktop
Homework Equations
I believe psi(x)= e^ikx+Re^-ikx in x<0
and psi(x)=Ae^iqx+Be^-iqx for x b/w o and a.
The Attempt at a Solution
My question is, since there is...
Just a quick question. Solving the Schrodinger equation (time-independent) for an infinite potential barrier, I end up with two wavefunctions.
In region I,
V(x)=0
\Rightarrow\psi(x)=Acos(\frac{\sqrt{2mE}}{\hbar}x)+Bsin(\frac{\sqrt{2mE}}{\hbar}x)
In region II,
V(x)=\infty...
Problem
An electron beam is sent through a potential barrier 4.5 \AA long. The transmission coefficient exhibits a third maximum at E = 100 \text{eV}. What is the height of the barrier?
Solution
Answer: 95.8219 \text{eV}
We know that the transmission coefficient reaches a maximum of 1 only...
Homework Statement
hey all! i have a relli urgent question that needs to be answered in as much detail as possible...hope someone can help...
Q: How is a particle, with energy of lower value than the potential barrier, able to penetrate through the barrier? (ans cannot have reasons like...
hi,...
i unfortunately couldn't find a solution to this problem although it seems like a classical textbook problem...
how can i solve the (time independent) schroedingerequation for the following potential
V(x) = \infty for x<=-1
V(x) = a\delta(x) for -1<x<1
V(x) = \infty for x>=1
so at x=0...
Hi,
I am doing simulations on a particle in some potential together with a fluctuating force and friction. To do that, I use the Langevin equation with the fluctuating force being a random number from a normal distribution with a temperature-dependent variance. I use a Verlet-algorithm for...
I am doing a computational project in my undergraduate Quantum Physics course on tunneling through a potential barrier. But, it's an irregular potential barrier, so I cannot simply use the results from a textbook. The first diagram, with corresponding wave equations, are shown in the first...
Homework Statement
find the wavefunction of a particle in a potential
V(x)= 0, |x|< a
V, |x|< b (V>0)
(Infinity), |x|>=b
ground state energy 0<=E<=V
Homework Equations
The Attempt at a Solution
i know the wavefunction has to be equal to zero at...
I am dealing with the classic problem of a potential barrier of finite width, with a particle tunneling through, in the case of E < V.
I am to calculate the transmission/reflection coefficients, and we first start off with the wavefunctions for the three regions.
Before the barrier, we...
I got a question about an infinite potential barrier. If a particle with a momentum p travell through an infinite potential barrier, how can the energy be conserved, thus how can the particle have the same momentum after passing the barrier? Does there exists any real life example?
If you have a Potential Barrier V (width a) and particles incident on left with energy E where E>V, are the following true:
Classical Physics:
- All particles will be transmitted past the barrier
- It cannot be reflected because that would mean it has negative E which is not possible...
If you have a Potential Barrier V (width a) and particles incident on left with energy E where E>V, are the following true:
Classical Physics:
- All particles will be transmitted past the barrier
- It cannot be reflected because that would mean it has negative E which is not possible...
The Coulomb potential barrier of a system of two nuclei X and Y is approximately given by VC = ZX*ZY*e2/RN where ZX and ZY are the charge numbers of the nuclei, e2 = 1.44 MeV*fm, RN = (AX1/3+AY1/3) × r0 is the sum of the nuclear radii. r0 is a constant usually estimated to 1.2 to 1.3 fm and AX...
I have a couple questions about finite potential barriers that I can't seem to figure out on my own...
1) Why does the real part of the wave function collapse inside the barrier (square, rectangular, barrier with V less than the energy of particle)? It seems to me that there should be some...
Since these seem to be popular around here these days, I thought I'd another to the mix :)
"A particle of mass m and energy E > 0 approaches a potential drop -V0 from the left. What is the probability that it will be reflected back if E = V0/3? The potential energy is V(x) = 0 for x<0 and...
Hi there,
Was wondering about the potential barrier problem when Eo>V. I have figured out the expression for the Transmission coeffient (after a lot of algebra) and am now wondering, what happens when I vary the width of the barrier, obviously there is greater transmission when the barrier...
(modified this to reflect a better understanding)
Stationary solutions to the wave equation mean that if I calculate <x> I will get a value independent of time. For a potential defined as V(x) =0 from x = 0 to a and infinite outside that range of x, the lowest energy solution is Psi(x,0) = A...