University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)
14th Edition
ISBN: 9780134265414
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 40, Problem 40.5E
(a)
To determine
The values of
(b)
To determine
The values of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
For a particle in a box, what would the probability distribution function Ic I2 look like if the particle behaved like a classical (Newtonian) particle? Do the actual probability distributions approach this classical form when n is very large? Explain.
Given: For sake of simplicity, let us consider a particle with mass, m, in one dimension trapped in an
infinite square well potential. The bottom of the potential well has zero potential energy, and the
particle is known to be confined between 0
Consider a particle of mass m, located in a potential energy well.one-dimensional (box) with infinite height walls. The wave function that describes this system is:Ψn(x) = K sin (nπx /L), for 0 ≤ x ≤ LΨn(x) = 0 for any other value.K is a constant and n = 1,2,3,... Determine K*K = │K│2
Chapter 40 Solutions
University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (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
- At time t = 0 the wave function for a particle in a box is given by the function in the provided image, where ψ1(x) and ψ1(x) are the ground-state and first-excited-state wave functions with corresponding energies E1 and E2, respectively. What is ψ(x, t)? What is the probability that a measurement of the energy yields the value E1? What is <E>?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_forwardA particle is described one-dimensionally on the real x axis, whose wave function is shown below, where L is a problem parameter (L > 0) and c is a real number.I) Determine the probability density function of this particle. Sketch a chart of it.II) Determine the constant c as a function of the parameter L.III) Calculate the probability of finding the particle in the region 0 ≤ x ≤ L.(With X=5 and Y=3)arrow_forward
- Imagearrow_forwardA particle is described by the wave function: Ψ(x)=b(a2-x2), for -a≤ x ≤ +a, and Ψ(x)=0 for -a ≥ x ≤ +a, where a and b are positive real constants. i) Using the normalization equation, find b in terms of a ii) What is the probability of finding the particle at x=+a/2 in the interval of width 0.010a? iii) What is the probability of finding the particle between x=+a/2 and x=+a?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_forward
- A 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_forwardConsider a particle in the first excited state of an infinite square well of width L. This particle has wavefunction (found in image ) for −L/2 ≤ x ≤ L/2, and ψ2(x) = 0 elsewhere. a) What is the value of the energy of this particle, E2? b) What is the probability density function, ρ, for this particle? c) At what values of x does the probability density vanish? d) What is the probability of finding this particle in the interval 0 ≤ x ≤ L/8?arrow_forward3 Solve this problem in a quantum canonical ensemble. We have a one-dimensional oscillator of mass m and frequency ω. Find the correct probability density associated with position x and discuss its values at the following limits kBT >> ℏω and kBT << ℏω. Finally, analyze the case of average energy and compare your result with the quantum mechanical result.arrow_forward
- Problem 1. Using the WKB approximation, calculate the energy eigenvalues En of a quantum- mechanical particle with mass m and potential energy V (x) = V₁ (x/x)*, where V > 0, Express En as a function of n; determine the dimensionless numeric coefficient that emerges in this expression.arrow_forwardProblem 3. Consider the two example systems from quantum mechanics. First, for a particle in a box of length 1 we have the equation h² d²v 2m dx² EV, with boundary conditions (0) = 0 and (1) = 0. Second, the Quantum Harmonic Oscillator (QHO) V = EV h² d² 2m da² +ka²) 1 +kx² 2 (a) Write down the states for both systems. What are their similarities and differences? (b) Write down the energy eigenvalues for both systems. What are their similarities and differences? (c) Plot the first three states of the QHO along with the potential for the system. (d) Explain why you can observe a particle outside of the "classically allowed region". Hint: you can use any state and compute an integral to determine a probability of a particle being in a given region.arrow_forwardWhich of the following is/are correct for the equation y(x) dx defined for a particle whose state function is y(x) (11) (iii) This equation gives the probability of the particle with the range x to X₂. This equation applies to the particle moving in any dimension. This equation defines relation between the state function and the probability with the range x; to x₂- (a) Only (1) (b) (ii) and (iii) (c) (i) and (iii) (d) (i) and (ii)arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning