Bundle: Physics For Scientists And Engineers With Modern Physics, Loose-leaf Version, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term
10th Edition
ISBN: 9781337888585
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Question
Chapter 40.1, Problem 40.1QQ
To determine
The value of
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The wave function of a particle in a one-dimensional
box of width L is u(x) = A sin (7x/L). If we know the
particle must be somewhere in the box, what must be
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Consider a particle with mass m in an infinite square well of width L = 1, with energy E
(a) What energy state n is this particle in?
(b) What is the probability that the particle is in the range
Chapter 40 Solutions
Bundle: Physics For Scientists And Engineers With Modern Physics, Loose-leaf Version, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term
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
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- If the potential is given in following figure, please draw a possible wave functions for E1 energy for the particle. (Uo> E1 >0) U 8. Uo E1arrow_forward2arrow_forwardConsider 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_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_forwardV (x) = 00, V(x) = 0, x<0,x 2 a 0arrow_forwardThe wave function of free particle initially at time t=0 is given by the wave packet $(x,0) = [2π(4x)3]-¹/4 exp{-4(4x)³ ikox} + ik where (Ax) represents the initial width of the wave packet (i.e. the variance). a) (x, t). b) Determine the wave function for the free particle at some later time t, What is the width (the variance) of the wave packet at the later time t?arrow_forwardA particle with mass m is moving in three-dimensions under the potential energy U(r), where r is the radial distance from the origin. The state of the particle is given by the time-independent wavefunction, Y(r) = Ce-kr. Because it is in three dimensions, it is the solution of the following time-independent Schrodinger equation dıp r2 + U(r)µ(r). dr h2 d EÞ(r) = 2mr2 dr In addition, 00 1 = | 4ar?y? (r)dr, (A(r)) = | 4r²p²(r)A(r)dr. a. Using the fact that the particle has to be somewhere in space, determine C. Express your answer in terms of k. b. Remembering that E is a constant, and the fact that p(r) must satisfy the time-independent wave equation, what is the energy E of the particle and the potential energy U(r). (As usual, E and U(r) will be determined up to a constant.) Express your answer in terms of m, k, and ħ.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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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