University Physics with Modern Physics (14th Edition)
14th Edition
ISBN: 9780321973610
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 40, Problem 40.6DQ
To determine
To explain: Why the values
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Calculate the probability that an electron will be found (a) between x = 0.1 and 0.2 nm, (b) between 4.9 and 5.2 nm in a box of length L = 10 nm when its wavefunction is Ψ = (2/L)1/2 sin(2πx/L). Treat the wavefunction as a constant in the small region of interest and interpret δV as δx.
An electron in a one-dimensional region of length L is described by the wavefunction ψn(x) = sin(nπx/L), where n = 1, 2, …, in the range x = 0 to x = L; outside this range the wavefunction is zero. The orthogonality of these wavefunctions is confirmed by considering the integralI= ∫0L sin(nπx/L)sin(mπx/L)dx(a) Use the identity sinAsinB = 1/2{cos(A-B)-cos(A+B)} to rewrite the integrand as a sum of two terms. (b) Consider the case n = 2, m = 1, and make separate sketch graphs of the two terms identified in (a) in the range x = 0 to x = L. (c) Make use of the properties of the cosine function to argue that the area enclosed between the curves and the x axis is zero in both cases, and hence that the integral is zero. (d) Generalize the argument for the case of arbitrary n and m (n ≠ m).
A quantum particle is described by the wave function ψ(x) = A cos (2πx/L) for −L/4 ≤
x ≤ L/4 and ψ(x) everywhere else. Determine:
Chapter 40 Solutions
University Physics with Modern Physics (14th Edition)
Ch. 40.1 - Does a wave packet given by Eq. (40.19) represent...Ch. 40.2 - Prob. 40.2TYUCh. 40.3 - Prob. 40.3TYUCh. 40.4 - Prob. 40.4TYUCh. 40.5 - Prob. 40.5TYUCh. 40.6 - Prob. 40.6TYUCh. 40 - Prob. 40.1DQCh. 40 - Prob. 40.2DQCh. 40 - Prob. 40.3DQCh. 40 - Prob. 40.4DQ
Ch. 40 - If a panicle is in a stationary state, does that...Ch. 40 - Prob. 40.6DQCh. 40 - Prob. 40.7DQCh. 40 - Prob. 40.8DQCh. 40 - Prob. 40.9DQCh. 40 - Prob. 40.10DQCh. 40 - Prob. 40.11DQCh. 40 - Prob. 40.12DQCh. 40 - Prob. 40.13DQCh. 40 - Prob. 40.14DQCh. 40 - Prob. 40.15DQCh. 40 - Prob. 40.16DQCh. 40 - Prob. 40.17DQCh. 40 - Prob. 40.18DQCh. 40 - Prob. 40.19DQCh. 40 - Prob. 40.20DQCh. 40 - Prob. 40.21DQCh. 40 - Prob. 40.22DQCh. 40 - Prob. 40.23DQCh. 40 - Prob. 40.24DQCh. 40 - Prob. 40.25DQCh. 40 - Prob. 40.26DQCh. 40 - Prob. 40.27DQCh. 40 - Prob. 40.1ECh. 40 - Prob. 40.2ECh. 40 - Prob. 40.3ECh. 40 - Prob. 40.4ECh. 40 - Prob. 40.5ECh. 40 - Prob. 40.6ECh. 40 - Prob. 40.7ECh. 40 - Prob. 40.8ECh. 40 - Prob. 40.9ECh. 40 - Prob. 40.10ECh. 40 - Prob. 40.11ECh. 40 - Prob. 40.12ECh. 40 - Prob. 40.13ECh. 40 - Prob. 40.14ECh. 40 - Prob. 40.15ECh. 40 - Prob. 40.16ECh. 40 - Prob. 40.17ECh. 40 - Prob. 40.18ECh. 40 - Prob. 40.19ECh. 40 - Prob. 40.20ECh. 40 - Prob. 40.21ECh. 40 - Prob. 40.22ECh. 40 - Prob. 40.23ECh. 40 - Prob. 40.24ECh. 40 - Prob. 40.25ECh. 40 - Prob. 40.26ECh. 40 - Prob. 40.27ECh. 40 - Prob. 40.28ECh. 40 - Prob. 40.29ECh. 40 - Prob. 40.30ECh. 40 - Prob. 40.31ECh. 40 - Prob. 40.32ECh. 40 - Prob. 40.33ECh. 40 - Prob. 40.34ECh. 40 - Prob. 40.35ECh. 40 - Prob. 40.36ECh. 40 - Prob. 40.37ECh. 40 - Prob. 40.38ECh. 40 - Prob. 40.39ECh. 40 - Prob. 40.40ECh. 40 - Prob. 40.41ECh. 40 - Prob. 40.42PCh. 40 - Prob. 40.43PCh. 40 - Prob. 40.44PCh. 40 - Prob. 40.45PCh. 40 - Prob. 40.46PCh. 40 - Prob. 40.47PCh. 40 - Prob. 40.48PCh. 40 - Prob. 40.49PCh. 40 - Prob. 40.50PCh. 40 - Prob. 40.51PCh. 40 - Prob. 40.52PCh. 40 - Prob. 40.53PCh. 40 - Prob. 40.54PCh. 40 - Prob. 40.55PCh. 40 - Prob. 40.56PCh. 40 - Prob. 40.57PCh. 40 - Prob. 40.58PCh. 40 - Prob. 40.59PCh. 40 - Prob. 40.60PCh. 40 - Prob. 40.61PCh. 40 - Prob. 40.62PCh. 40 - Prob. 40.63PCh. 40 - Prob. 40.64CPCh. 40 - Prob. 40.65CPCh. 40 - Prob. 40.66CPCh. 40 - Prob. 40.67PPCh. 40 - Prob. 40.68PPCh. 40 - Prob. 40.69PPCh. 40 - Prob. 40.70PP
Knowledge Booster
Similar questions
- Can we simultaneously measure position and energy of a quantum oscillator? Why? Why not?arrow_forwardAn electron has a wavefunction ψ(x)=Ce-|x|/x0 where x0 is a constant and C=1/√x0 for normalization. For this case, obtain expressions for a. ⟨x⟩ and Δx in terms of x0. b. Also calculate the probability that the electron will be found within a standard deviation of its average position, that is, in the range ⟨x⟩-∆x to ⟨x⟩+∆x, and show that this is independent of x0.arrow_forwardHarmonic oscillator eigenstates have the general form 1 μω ,1/4 μω AG)(√(-) n ħ In this formula, which part determines the number of nodes in the harmonic oscillator state? = y (x) 1 √(™ ћn 2"n! Holev 1/4 μω 1 2"n! exp(-1022²) 2ħ μω ħ 2"n! exp μω χ 2ħ 2arrow_forward
- (a) Let n = a + ib be a complex number, where a and b are real (positive or negative) numbers. Show that the product nn* is always a positive real number. (b) Let m = c + id be another complex number. Show that |nm| = |n| |m|.arrow_forwardConsider a macroscopic object of mass 90 grams confined to move between two rigid walls separated by 2 m. What is the minimum speed of the object? What should the quantum number n be if the object is moving with a speed 1 ms-1? What is the separation of the energy levels of the object moving with that speed?arrow_forwardWhen an electron trapped in a one-dimensional box transitions from its n= 2 state to its n= 1 state, a photon with a wavelength of 9 nm is emitted. What is the length of the box (in nm)? What If? If electrons in the box also occupied the n= 3 state, what other wavelengths of light (in nm) could possibly be emitted? Enter the shorter wavelength first.arrow_forward
- A certain atom requires 3.0 eV of energy to excite an electron from the ground level to the first excited level. Model the atom as an electron in a box and find the width L of the box.arrow_forwardThe treatment of electrons in atoms must be a quantum treatment, but classical physics still works for baseballs. Where is the dividing line? Suppose we consider a spherical virus, with a diameter of 30 nm, constrained to exist in a long, narrow cell of length 1.0 μm. If we treat the virus as a particle in a box, what is the lowest energy level? Is a quantum treatment necessary for the motion of the virus?arrow_forwardThe wavefunction for v =1 for a simple harmonic oscillator is Ψ = (2)1/2 ( α3/π)1/4 x exp (-αx2/2) Find the values of x such that ψ* ψ is a maximum.Hint: Differentiate dψ*ψ/dx and set the result equal to zero and solve for the value of x.arrow_forward
- The energy eigenvalues of a particle in a 3-D box of dimensions (a, b, c) is given by E (nx, ny, nz) -2²² (²²² +²2² +²2²) (a) Ten protons are confined in a box of dimension (a, 2a, a) on each side. Calculate the total energy of the ground state of these ten protons if we assume that the protons don't interact with each other. (b) If the ten protons are replaced by 10 neutral hydrogen atoms in the ground state, calculate the total 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. An electron in a long organic molecule used in a dye laser behave approximately like a particle in a box with width 4.18 nm. (a) What is the λ of the proton emitted when the electron undergoes a transition from the first excited level to the ground level. (b) What is the λ of the proton emitted when electron undergoes a transition from the second excited level to the first excited level?arrow_forwardA particle of mass 1.60 x 10-28 kg is confined to a one-dimensional box of length 1.90 x 10-10 m. For n = 1, answer the following. (a) What is the wavelength (in m) of the wave function for the particle? m (b) What is its ground-state energy (in eV)? eV (c) What If? Suppose there is a second box. What would be the length L (in m) for this box if the energy for a particle in the n = 5 state of this box is the same as the ground-state energy found for the first box in part (b)? m (d) What would be the wavelength (in m) of the wave function for the particle in that case? marrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax