Answered: Question: Particles with energy Ea. | bartleby

Related questions

Question

Question:

Particles with energy E<Vo are incident on a potential barrier of height Vo of the form (see image).

Find the wave function of all three regions and the transmission probability of the region x<0, x>a.

if x < 0
V (x)
ν% if 0<x< α .
if x >α

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Calculate the uncertainties dr = V(x2) and op = V(p²) for %3D a particle confined in the region -a a, r<-a. %3D
At time t = 0 a particle is described by the one-dimensional wave function 1/4 (a,0) = (²ª) e-ikre-ar² where k and a are real positive constants. Verify that the wave function (r, 0) is normalised. Hint: you may find the following standard integral useful: Loze -2² dx = √,
The quantum mechanical tunneling process occurs if an electron is incident on a potential barrier of finite width a and finite height Uo. Calculate the transmission probability for this case assuming a barrier width a=1.4 nm and a barrier height Uo=2.6eV assuming that the energy of the electron is E=2.2eV. Give your result in % and round it off to two decimal places, i.e. the nearest hundredths. U(x) Uo 0 < E < Uo E 01 a
Consider a 6-functional potential well U(x) = -V8(r - a) spaced by the distance a from an infinite potential barrier U(r) o at x < 0, as shown in the figure below. Obtain an equation for the energy level Eg of a bouud state in the well. Using this equalion, find the minimum distance ae of the well from the barrier at which the bound state in the well disappears for all a < ac. Infinite potential barrier Energy level of a bound state - E, U(z) = -V6(r – a)-
4. a) Consider a square potential well which has an infinite barrier at x = 0 and a barrier of height U at x = L, as shown in the figure. For the case E L) that satisfy the appropriate boundary conditions at x = 0 and x = o. Put the appropriate conditions on x = L to find the allowed energies of the system. Are there conditions for which the solution is not possible? explain. U E L.
Problem 15. In the case of a particle tunneling through the barrier, we made equal both functions and derivatives at the boundary between region I and II, and between II and III, see eq. (9a – 9d). But in the case of the particle in the box, we made both functions equal at x = 0 and at x = L. Explain why we did not consider derivatives in this case.