Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 5, Problem 71E
To determine
To prove
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A particle with mass m is moving along the x-axis in a potential given by the potential energy
function U(x) = 0.5mw²x². Compute the product (x, t)*U (x) V (x, t). Express your
answer in terms of the time-independent wave function, (x).
Answer the following about an observable that is represented by the operator
 = wo (3² + 3²).
ħ
(4)
Is it possible to write a complete set of basis states that are simultaneously eigenstates of the operator
Ĵ and Â? If so, explain how you know. If not, write an uncertainty principle for the observables A
and J.
A particle of mass m confined to an infinite potential well of length L from x= 0 to x=L is in the ground state.
(a) Is this state an eigenfunction of the momentum operator, px? Justify your answer.
(b) If an observation of momentum is made, what value, or values, could be obtained? Justify your answer.
Chapter 5 Solutions
Modern Physics
Ch. 5 - Prob. 1CQCh. 5 - Prob. 2CQCh. 5 - Prob. 3CQCh. 5 - Prob. 4CQCh. 5 - Prob. 5CQCh. 5 - Prob. 6CQCh. 5 - Prob. 7CQCh. 5 - Prob. 8CQCh. 5 - Prob. 9CQCh. 5 - Prob. 10CQ
Ch. 5 - Prob. 11CQCh. 5 - Prob. 12CQCh. 5 - Prob. 13CQCh. 5 - Prob. 14CQCh. 5 - Prob. 15CQCh. 5 - Prob. 16CQCh. 5 - Prob. 17CQCh. 5 - Prob. 18CQCh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Prob. 30ECh. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - Prob. 33ECh. 5 - Prob. 34ECh. 5 - Prob. 35ECh. 5 - Prob. 36ECh. 5 - Prob. 37ECh. 5 - Prob. 38ECh. 5 - Prob. 39ECh. 5 - Prob. 40ECh. 5 - Prob. 41ECh. 5 - Prob. 42ECh. 5 - Obtain expression (5-23) from equation (5-22)....Ch. 5 - Prob. 44ECh. 5 - Prob. 45ECh. 5 - Prob. 46ECh. 5 - Prob. 47ECh. 5 - Prob. 48ECh. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - Prob. 53ECh. 5 - Prob. 54ECh. 5 - Prob. 55ECh. 5 - Prob. 56ECh. 5 - Prob. 57ECh. 5 - Prob. 58ECh. 5 - Prob. 59ECh. 5 - Prob. 60ECh. 5 - Prob. 61ECh. 5 - Prob. 62ECh. 5 - Prob. 63ECh. 5 - Prob. 64ECh. 5 - Prob. 65ECh. 5 - Prob. 66ECh. 5 - Prob. 67ECh. 5 - Prob. 68ECh. 5 - Prob. 69ECh. 5 - Prob. 70ECh. 5 - Prob. 71ECh. 5 - In a study of heat transfer, we find that for a...Ch. 5 - Prob. 73CECh. 5 - Prob. 74CECh. 5 - Prob. 75CECh. 5 - Prob. 76CECh. 5 - Prob. 77CECh. 5 - Prob. 78CECh. 5 - Prob. 79CECh. 5 - Prob. 80CECh. 5 - Prob. 81CECh. 5 - Prob. 82CECh. 5 - Prob. 83CECh. 5 - Prob. 84CECh. 5 - Prob. 85CECh. 5 - Prob. 86CECh. 5 - Prob. 87CECh. 5 - Prob. 88CECh. 5 - Consider the differential equation...Ch. 5 - Prob. 90CECh. 5 - Prob. 91CECh. 5 - Prob. 92CECh. 5 - Prob. 93CECh. 5 - Prob. 94CECh. 5 - Prob. 95CECh. 5 - Prob. 96CECh. 5 - Prob. 97CECh. 5 - Prob. 98CE
Knowledge Booster
Similar questions
- Consider a particle in a box of length L with one end coinciding with the origin. Consider the initial state to be given by the wavefunction: ψ(x,0)=Asin2nπx/L for 0≤x≤L/2 and ψ(x,0)=0 for x>L/2. 1. Normalize this wavefunction. 2. Compute the time evolution of this system. 3. Find the probability of measuring Ei at some time t.arrow_forwardConsider the function v(1,2) =( [1s(1) 3s(2) + 3s(1) 1s(2)] [x(1) B(2) + B(1) a(2)] Which of the following statements is incorrect concerning p(1,2) ? a. W(1,2) is normalized. Ob. The function W(1,2) is symmetric with respect to the exchange of the space and the spin coordinates of the two electrons. OC. y(1,2) is an eigenfunction of the reference (or zero-order) Hamiltonian (in which the electron-electron repulsion term is ignored) of Li with eigenvalue = -5 hartree. d. The function y(1,2) is an acceptable wave function to describe the properties of one of the excited states of Lit. Oe. The function 4(1,2) is an eigenfunction of the operator S,(1,2) = S;(1) + S,(2) with eigenvalue zero.arrow_forwardLet's consider a harmonic oscillator. The total energy of this oscillator is given by E=(p²/2m) +(½)kx?. A) For constant energy E, graph the energies in the range E to E + dE, the allowed region in the classical phase space (p-x plane) of the oscillator. B) For k = 6.0 N / m, m = 3.0 kg and the maximum amplitude of the oscillator xmax =2.3 m For the region with energies equal to or less than E, the oscillator number of states that can be entered D(E).arrow_forward
- The eigenstates of the particle-in-a-box are written, n = √ sin (™T). If L = 10.0, what is the expectation value for the quantity 2ħ² + p² in the n = 3 eigenstate? Report your answer as a multiple of ħ². (Note: ô = −iħª) d dx'arrow_forwardAssume that you have a quantum mechanical observable N with eigenvalues Wi and corresponding eigenvectors |w;). Show that (n?) – (N)² where P(w;) is the probability of measuring the eigenvalue w; for some quantum state.arrow_forwardLet's consider the two-qubit state 3 |) = 100)+101) +110). a) Find the expectation values for the values of both qubits separately. b) The product of qubit values is represented by the operator b₁b2 = (ô× 1) (I Øô) = (ô ❀ô), where bn is the observable for the value of qubit n. Find the expectation value for the product. For statistically independent quantities the expectation value of their product is the product of their expectation values. Are the values of the qubits correlated in state |V)? c) Show that the state cannot be expressed as a product state, i.e., it is an entangled state.arrow_forward
- A qubit is initially in state [0). Its state is then transformed by the unitary operation represented by the matrix U ¹ = ¹2 ( √3³ √ ) = √³ (10) (0) + (1¹) (11) + ½ (10) (1| + (1) (01) . a) What is the probability of the qubit to have the value 0 when measured before the transforma- tion? How about the value 1? b) What is the probability of the qubit to have the value 0 when measured after the transforma- tion? How about the value 1? c) Let's say that the qubit is measured after the transformation, and its value is found to be 1. What is the probability of the qubit to have the value 0 immediately after the measurement?arrow_forwardWhat would happen to the incident wave Þ(x) = Aelk* at x < 0 that sees a step potential in the form V(x) = iT in the positive x region? Here i is complex number and I is positive real number. (a) Explain in detail (perform some calculations too). (b) Calculate the reflection and transmission coefficients.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_forward
- Using the eigenvectors of the quantum harmonic oscillator, i.e., n >, find the matrix element ,where Pis the momentum operator. 11mwh 2 9mwh 2 iv5mwh iv6mwharrow_forwardWe have a free particle in one dimension at a time t = 0, the initial wave function is V (x,0) = Ae-r|æ| where A and r are positive real constants. Find ø(k).arrow_forwardFind the probabilities that a particle can be found between x = 0.45 and 0.55 when the particle in limited to the x axis and has wave function. ψ = {ax, 0 ≤ x ≤ 1 ; 0, x< 0 and x >1. Also find the average (expectation value) of x.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:PEARSON
Introduction 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