Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 40, Problem 11P
(a)
To determine
The expectation value of
(b)
To determine
The probability of finding the particle near
(c)
To determine
The probability of finding the particle near
(c)
To determine
To justify that the result of part (a) does not contradict the results of parts (b) and (c).
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
For a quantum particle of mass m in the ground state of a square well with length L and infinitely high walls, the uncertainty in position is Δx ≈ L. (a) Use the uncertainty principle to estimate the uncertainty in its momentum.(b) Because the particle stays inside the box, its average momentum must be zero. Its average squared momentum is then ⟨p2⟩ ≈ (Δp)2. Estimate the energy of the particle. (c) State how the result of part (b) compares with the actual ground-state energy.
A quantum particle in an infinitely deep square well has a wave function given by ψ2(x) = √2/L sin (2πx/L)for 0 ≤ x ≤ L and zero otherwise. (a) Determine the expectation value of x. (b) Determine the probability of finding the particle near 1/2 L by calculating the probability that the particle lies in the range 0.490L ≤ x ≤ 0.510L. (c) What If? Determine the probability of finding the particle near 1/4L bycalculating the probability that the particle lies in the range 0.240L ≤ x ≤ 0.260L. (d) Argue that the result of part (a)does not contradict the results of parts (b) and (c).
The wave function for a quantum particle is
a
4(x)
π (x² + a²)
for a > 0 and -*
Chapter 40 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 40.1 - Prob. 40.1QQCh. 40.2 - Prob. 40.2QQCh. 40.2 - Prob. 40.3QQCh. 40.5 - Prob. 40.4QQCh. 40 - Prob. 1PCh. 40 - Prob. 2PCh. 40 - Prob. 3PCh. 40 - Prob. 4PCh. 40 - Prob. 5PCh. 40 - Prob. 6P
Ch. 40 - Prob. 7PCh. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - Prob. 13PCh. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Prob. 16PCh. 40 - Prob. 17PCh. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 23PCh. 40 - Prob. 24PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Prob. 28PCh. 40 - Prob. 29PCh. 40 - Two particles with masses m1 and m2 are joined by...Ch. 40 - Prob. 31APCh. 40 - Prob. 32APCh. 40 - Prob. 33APCh. 40 - Prob. 34APCh. 40 - Prob. 36APCh. 40 - Prob. 37APCh. 40 - Prob. 38APCh. 40 - Prob. 39APCh. 40 - Prob. 40APCh. 40 - Prob. 41APCh. 40 - Prob. 42APCh. 40 - Prob. 44CPCh. 40 - Prob. 46CPCh. 40 - Prob. 47CP
Knowledge Booster
Similar questions
- Suppose a wave function is discontinuous at some point. Can this function represent a quantum state of some physical particle? Why? Why not?arrow_forwardA quantum particle in an infinitely deep square well has a wave function that is given by ψ1(x) = √2/Lsin (πx/L)for 0 ≤ x ≤ L and is zero otherwise. (a) Determine the probability of finding the particle between x = 0 and x = 1/3L.(b) Use the result of this calculation and a symmetry argumentto find the probability of finding the particle between x = 1/3 L and x = 2/3 L. Do not re-evaluate the integral.arrow_forward(a) Find the normalization constant A for a wave function made up of the two lowest states of a quantum particle in a box extending from x= 0 to x = L: x) = A sin + 4 sin L. (b) A particle is described in the space -aSxs a by the wave function (x) = A cos + B sin 2a a Determine the relationship between the values of A and B required for normalization.arrow_forward
- For a quantum particle described by a wave function (x), the expectation value of a physical quantity f(x) associated with the particle is defined by For a particle in an infinitely deep one-dimensional box extending from x = 0 to x = L, show that L 2n°7arrow_forwardFor a "particle in a box" of length, L, the wavelength for the nth level is given by An 2L %3D 2п and the wave function is n(x) = A sin (x) = A sin (x). The energy levels are пп %3D n?h? given by En : %3D 8mL2 lPn(x)|2 is the probability of finding the particle at position x in the box. Since the particle must be somewhere in the box, the integral of this function over the length of the box must be equal to 1. This is the normalization condition and ensuring that this is the case is called “normalizing" the wave function. Find the value of A the amplitude of the wave function, that normalizes it. Write the normalized wave function for the nth state of the particle in a box.arrow_forwardWhat is the probability of the particle that in the box with a length of 2 nm is between x = 0.2 and x = 1.0 nm? Ѱ=√(2/L)*sin(nπx/L)arrow_forward
- 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:(a) The normalization constant A,(b) The probability of finding the electron between x = 0 and x = L/8.arrow_forwardFor a particle in a one-dimensional box, calculate the probability of the particle to exists between the length of 0.30L and 0.70L if n = 5.arrow_forwardA wave function has the value A sin x between x= 0 and π but zero elsewhere. Normalize the wave function and find the probability that the particle is (a) between x = 0 and x = π/4 and (b) between x= 0 and π/2.arrow_forward
- The wave function of a particle at t = 0 is given as: ψ(x, t) = C exp[ -|x|/x0] where C and x0 are constants. (a) What is the relation between C and x0?(b) Calculate the expectation value of position x of the particle.(c) Suggest a region in x in which the probability of finding the particle is 0.5.arrow_forwardWe are going to use Heisenberg's uncertainty principle to estimate the ground- state energy of hydrogen. In our model, the electron is confined in a one- dimensional well with a length about the size of hydrogen, so that Ax = 0.0529 nm. Estimate Ap, and then assume that the ground-state energy is roughly Ap2/2me. (Give your answer in Joules or electron-volts.)arrow_forwardThe wave function of a certain particle is y= A cos²x for -t/2 < xarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_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 with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher: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 with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax