Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 8.1, Problem 8.3P
To determine
The best bound on
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
For Problem 8.16, how do I prove the relations and give the correct expressions?
Consider the "step" potential:
V(x) =
(a) Calculate the reflection coefficient, for the case E 0.
(b) Calculate the reflection coefficient for the case E > Vo.
(c) For a potential such as this, which does not go back to zero to the right of
the barrier, the transmission coefficient is not simply |F12/A2 (with A the
-Vo
AV(x)
Scattering from a "cliff"
incident amplitude and F the transmitted amplitude), because the transmitted
wave travels at a different speed. Show that
T =
E-Vo F1²
E |A|²
X
for E> Vo. Hint: You can figure it out using Equation
gantly, but less informatively-from the probability current (
What is T, for E Vo, calculate the transmission coefficient for the step potential, and
check that T + R = 1.
Show that a gaussian psi (x) = e ^(-ax^2) can be an eigenfunction of H(hat) for harmonic oscillator
1. Compute T(hat)*psi
2. Compute Vhat* psi - assume V operator is 1/2w^2x^2
3. Write out Hbar*psi and identify terms so Hber*psi=E*psi is true
4. From cancellation find a
5. insert back a to Schrodinger eq above and find E
Chapter 8 Solutions
Introduction To Quantum Mechanics
Knowledge Booster
Similar questions
- Problem 1. The Morse potential, which is often used to model interatomic forces can be written in the form U(r) = D(1-e²²(²-))² 3 wherer is the distance between the two atomic nuclei. Determine the "spring constant" for small displacements from equilibrium for the Morse potential.arrow_forwardProve that the first three Legendre polynomials satisfy the Legendre equation when m = 0.arrow_forwardLet V = (xy, xy, (x−y)z). V is solenoidal. Use the homotopy or cone operator method to find a vector potential for it. Is your answer unique? If not, what is the most general vector potential for V?arrow_forward
- For Problem 8.37, how do I find <1/r> within the integral? I think that the exponent function inside of P(r) is actually troublesome to finding what I need to find; however, I am not certain of what's really the correct procedure here.arrow_forwardProblem 10.10 Consider a central force given by F(r) = -K/r³ with K > 0. Plot the effective potential and discuss possible types of motion.arrow_forwardIs the function 1/r a legitimate velocity potential in planepolar coordinates? If so, what is the associated stream functionψ(r, θ)?arrow_forward
- A system with charge (number of electrons) is placed in an electric field with potential E (volts). Express the general form (derivative expression) of Gibbs free energy function.arrow_forwardI need the answer as soon as possiblearrow_forwardhi... This question is about analytical mechanics. Show that the forces below(a,b) are conservative forces.and obtain the potential function for each. The a.,b forces are displayed in the uploaded photo.arrow_forward
- A potential Vo(0) = k sin² (0/2) (k is a constant) is present on the surface of a hollow sphere ofradius R.1. Find the potential Vout(r, 0) outside the sphere (i.c., for r > R).arrow_forwardFind the Expression for the Energy Eigenvalues, En. Needs Complete solution with 100% accuracy.arrow_forwardSubject : Mathematical Physics Write the power series (about the origin) of the following functions. Use Theorem III to find the disk of convergence of each series. What you are looking for is the point (anywhere in the complex plane) nearest the origin, at which the function does not have a derivative. Then the disk of convergence has center at the origin and extends to that point. The series converges inside the disk.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON