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 9, Problem 9.18P
(a)
To determine
The energy of the ground state, measured up from the bottom of the well.
(b)
To determine
Introduce a perturbation
(c)
To determine
The tunneling factor
(d)
To determine
The value of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
PROBLEM 2. Consider a spherical potential well of radius R and depth Uo,
so that the potential is U(r) = -Uo at r R.
Calculate the minimum value of Uc for which the well can trap a particle
with l = 0. This means that SE at Uo > Uc has at least one bound ground
state at l = 0 and E < 0. At Ug = Uc the bound state disappears.
Problem # 2.
In the two-level system, estimate the emission line full width at half maximum (FWHM) for
spontaneous emission at 650 nm if the spontaneous radiative lifetime of the upper state is about
3,000 nanoseconds.
Could someone explain to me in detail why bringing a crystal substance to absolute zero isn't possible?
I know it's not because of quantum mechanics and uncertainty like some people say, because particals at their lowest zero-point will have a temperature of exactly 0 K, even though they're still experiencing motion.
From what I've gathered, the energy or time required to pull it off is infinite, but I can't find any equations or clear explanations as to why or how that is. And I also don't know if there's any other reasons beyond that.
If you could give me a thourough a breakdown for how absolute zero is impossible as you possibly could, I'd greatly appreciate it.
Take as much extra time as you need. As long as it's detailed and correct I'm happy. Though ideally I would before it come in before the end of the day.
Chapter 9 Solutions
Introduction To Quantum Mechanics
Knowledge Booster
Similar questions
- TRQ. 3.1 Solve completely the following Quantum problem. Need full detailed answer, equations and if possible, theory/ literature. Question: A particle of spin 1 and a particle of spin 1/2 are in a configuration for which the total spin is equal to 1/2. If one were to measure the z-component of the spin of the particle with spin = 1, what values might one get and what are the probabilities associated with those values? Use Clebsch-Gordan table. Write the total spin state |s,ms> as linear combinations of |s1, ms1> |s2, ms2> states.arrow_forwardConsider a single electron confined to a one-dimensional quantum well device of length L = 0.5 nm. The quantum well device acts as a “trap” for the electron 1.What are the boundary conditions for this system? Apply them to show that ψn(x) = Asin(nπx/L), n = 1,2,3,... (check image) 2.Normalize the wave function to find the constant A. 3. Sketch ψ1, ψ2, and ψ3, as well as |ψ1|2, |ψ2|2, and |ψ3|2, and evaluate the energy levels E1, E2, and E3 in eV. 4. Suppose the particle is in the first excited state. What is the probability of finding the particle between x = L/4 and x = 3L/4? 5. Suppose, instead of one electron, we trap five electrons in the quantum well. Draw an energy-level diagram to show the electron configuration of the ground state. What is the ground state energy?arrow_forwardPhysics Department PHYS4101 (Quantum Mechanics) Assignment 2 (Fall 2020) Name & ID#. A three-dimensional harmonic oscillator of mass m has the potential energy 1 1 1 V(x.y.2) = ; mw*x² +mwży² +=mw;z? where w1 = 2w a. Write its general eigenvalues and eigenfunctions b. Determine the eigenvalues and their degeneracies up to the 4th excited state c. The oscillator is initially equally likely found in the ground, first and second excited states and is also equally likely found among the states of the degenerate levels. Calculate the expectation values of the product xyz at time tarrow_forward
- 1 W:0E Problem 1.17 A particle is represented (at time t = 0) by the wave function | A(a? – x²). if -a < x < +a. 0, Y (x, 0) = otherwise. (a) Determine the normalization constant A. (b) What is the expectation value of x (at time t = 0)? (c) What is the expectation value of p (at time t = 0)? (Note that you cannot get it from p = md(x)/dt. Why not?) (d) Find the expectation value of x². (e) Find the expectation value of p?. (f) Find the uncertainty in x (ox).arrow_forwardA particle with a size just below r* is unstable but a particle with a size 2) just above r* is stable. What comments would you make on this statement? If you agree then, why are the particles just above (very little bigger than r*) a critical size r* thermodynamically stable even though the energy (Gibbs free energy) is positive. a) A 4G, surface energy 4xr'y AG Volume free energy Excess free energy AG. b) Why the free energy vs particle radius curves for homogeneous and heterogeneous nucleation differs. CAG, AG AG JAGeter AGomaarrow_forwardA one-dimensional infinite potential well has a length of 2L. What are the energy eigenvalues? Calculate the ground state energy if ten protons are confined in the box. Assume that the protons don’t interact with each other. If the ten protons are replaced by ten neutral hydrogen atoms, what is the total ground state energy resulting from the confinement? Again, assume that the hydrogen atoms do not interact with each other. You can treat the mass of proton and hydrogen atom to be identical.arrow_forward
- PROBLEM 2. The potential energy of a weakly anharmonic oscillator can be modeled by: m U(x) P²+Bx*, where the last quatric term describes a small anharmonic correction. The energy levels En of the anharmonic oscillator in the first order in the pa- rameter 3 are given by: En = hw 5) + B(n|z*\n). Calculate the energy of the ground state Eo of the anharmonic oscillator.arrow_forward4.8. The energy eigenfunctions V1, V2, V3, and 4 corresponding to the four lowest energy states for a particle confined in the finite potential well = {0 V(x) = -Vo |x| a/2 are sketched in Fig. 4.4. For which of these energy eigenfunctions would the probability of finding the particle outside the well, that is, in the region [x] > a/2, be greatest? Explain. Justify your reasoning using the solution to the Schrödinger equation in the region x > a/2.arrow_forwardA particle in a box is in the ground level. What is the probability of finding the particle in the right half of the box? (Refer to Fig. , but don’t evaluate an integral.) Is the answer the same if the particle is in an excited level? Explain.arrow_forward
- Problem 7. 1. Calculate the energy of a particle subject to the potential V(x) = Vo + câ?/2 if the particle is in the third excited state. 2. Calculate the energy eigenvalues for a particle moving in the potential V(x) = câ2/2+ bx. %3!arrow_forwardThe wave function of a particle in two dimensions in plane polar coordinates is given by: T ¥(r,0) = A. r. sin0exp[- where A and ao are positive real constants. 1. Find the constant A A using the normalization condition in the form SS |¥(r,0)|²rdrd0 = 1 2. Calculate the expectation values of r, and ². 3. Assuming that the momentum operator in plane polar coordinate is giving in the form ħa p = calculate the expectation values of p and p². 1 Ər' 4. Find the standard deviations of r and p and show that their product is consistent with the Heisenberg uncertainty principle.arrow_forwardWhat is the Born interpretation of the wave function? Use formula, where applicable. Given that a solution to Schrodinfer Equation (SE) is: Y = eikx=coskx + i sin kx, where k = (2mE/h2)1/2arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity 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 LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege 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