Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 7, Problem 15P
To determine
The transmission coefficient for each of the individual barrier also prove that the form of Equation 7.10 is recovered in the case where
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Recall the signal-plus-noise model
X; = St + v1,
where s; is the nonrandom siginal series and v; iz the zero-mean noise time series (NOT necessarily white
noise).
Suppose the autocorrelation function (ACF) of {v;} is given by p,(s, t). What is the ACF px(s, t) for {x; }?
Confirm your answer.
Answer all these questions
Q1: A one dimensional potential barrier is shown in the figure below. Calculate the transmission
coefficient.
E
E >V1 > V2
V1
V2
x=0
x= a
With wavefuction in each region as follow:
41(x) = eikix + Be¬ik1x,
%3D
42(x) = Cek2* + De-ik2*,
And
3(x) = Eeik3x
%3D
Then use: h = 6.625 10-34Js, m = 9.109 10-31Kg, e = 1.602 10-19, E = 5 e, V1 = 0.6 E, V2 =
%3D
2mE
E, k2 =
2m(E-V1)
,k3
2m(E-V2)
0.4 E, k, :
to find the value transmission coefficient.
Knowledge Booster
Similar questions
- Q.18. Verify the statement in the text that, if the phase velocity is the same for all wavelengths of a certain wave phenomenon (that is, there is no dispersion), the group and phase velocities are the same?arrow_forwardConsider the Gaussian wave packet, 6(x) = A exp 1 Por (1) where Po and & are real parameters. a. Show that this wave function can be normalized, dr v(r)² = 1, (2) %3D and find the corresponding amplitude A. b. Find the corresponding wave function, (p), in the momentum repre- sentation and check its normalization. c. Calculate expectation values (r) and (p). d. Calculate the uncertainties Ar and Ap and their product.arrow_forwardConsider the Gaussian wave packet, (x) = A exp Por 452 where po and & are real parameters. a. Show that this wave function can be normalized, dr ļú(2)* = 1, and find the corresponding amplitude A. b. Find the corresponding wave function, o(p), in the momentum repre- sentation and check its normalization. c. Calculate expectation values (r) and (p). d. Calculate the uncertainties Ar and Ap and their product.arrow_forward
- Consider a particle with function : (image) Normalize this function. Qualitatively plot the probability distribution function in terms of x. Where is it most likely to find a particle? Find the expected value of the place and compare it with part C.arrow_forwardFind the locations where the probability density has its maximum values for the wave function w(x) = A(2ax² - 1)e-ax2/2, which represents the second excited state of the simple harmonic oscillator. Iarrow_forwardC3arrow_forward
- Q.4. Imagine that a particle is coming from left with finite energy E and encountered a potential V(x) = Vo (> E) at origin for x20 (as shown below in the figure). Prove that if Vo goes to infinity then wave function goes to zero in the region x 20. IF Vo X-0arrow_forwardA wavefunction can be written as A cos x + B sin x. It can also be written as Ceix + De-ix. Express C and D in terms of A and B.arrow_forwardProblem1 : a. Show that group velocity can be expressed as dvp vg = Up di b. Find the group velocity for plane waves in a dispersive medium, for which v, = A + BA, where A and B are constants. Interpret the result.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning