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 2P
(a)
To determine
Sketch the function for the values of x in the interval
(b)
To determine
The value of A.
(c)
To determine
The probability that the particle will be found in
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
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.
(a) Use the standard definition of the average value of a random variable given its
probability density function:
= 10 x p₁(x)
-∞
(9)
to find average position of the wave-particle for each stationary state. Recall
that pn =
Un is the probability density associated with the stationary state
n = 1,2,... for the particle in a box. Also, n(x, t) is only defined for x =
(0, L). Hint: the result is the same for all stationary states. That is, it does
not depend on n.
n=
dx.
V (x) = 00,
V(x) = 0,
x<0,x 2 a
0
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
- 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│2arrow_forwardConsider a one-dimensional particle which is confined within the region 0≤x≤a and whose wave function is (x, t) = sin (x/a) exp(-iwt). (D) v sv (a) Find the potential V(x). (b) Calculate the probability of finding the particle in the interval a/4 ≤x≤3a/4.arrow_forward2arrow_forward
- Consider a particle with the following wave-function: ,xL and L and A are constants. (a) What is the normalization constant A (in terms of L)? (b) What is (in terms of L)? ? (ie, ) (c) What is the probability that the particle will be found within x=0 and L/2?arrow_forwardParticle is described by the wave function Y = 0,x 0 a) Calculate A. b) Take L as 10 nm and calculate the probability of finding the particle in the region 1 nmarrow_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_forwardU = U, %3D U = 0 X = 0 A potential step U(x) is defined by U(x) = 0 for x 0 If an electron beam of energy E > U, is approaching from the left, write the form of the wave function in region I (x 0) in terms of the electron mass m, energy E, and potential energy U,. Do not bother to determine the constant coefficients. Formulas.pdf (Click here-->) Edit Vicw Insert Format Tools Table 12pt v Paragraph BIU Av eu T? varrow_forwardA free particle moving in one dimension has wave function Ψ(x, t)= A[ei(kx-vt)- ei(2kx-vt)]where k and v are positive real constants.Calculate vav as the distance the maxima have moved divided by the elapsed time.arrow_forwardAt t = 0, a particle is prepared to assume the state V(x,0) = ¹+2i₁(x) + cos (²) sin( ³ )&₂(x) + A¥3(x) where A is a constant and the eigenfunctions ₁(x), 2(x), and 3(x) correspond to energies E₁, E2, and E3, respectively. What is the probability that the particle has energy E3? a. 0.822 b. 0.325 c. 0.675 d. 0.570arrow_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_forwardAt a certain instant of time, a particle has the wave function y (x) A xe(- |x|/B where b — 3 пт: а) Normalize the function. If at that instant a measurement of x is made, find the probability that the result: b) is between 0.9000 and 0.9001 nm, is between O and 2 nm. c) For what value of x is the probability density minimal?arrow_forward2. a) Show that for state n = 0 of a harmonic oscillator whose classical amplitude of motion is A, y = 1 when evaluated at x = A, where y is the quantity defined by the equation 1/2 /km 2amv y = b) Find the probability density %|²dx at x 0 and at x=±A de un oscilador armónico en su estado n=0.arrow_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
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