Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
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Chapter 35, Problem 13P
(a)
To determine
The wavenumber
(b)
To determine
The graph of the reflection coefficient
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For a region where the potential V = 0, the wave function is given by √2/∝ sin (3πx/∝). Calculate the energy of this system
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Consider the wave function V(x, t) = A(cos (A)) e-jot for – 1
(a) Write the wave function w(x)= wo•e'kx in the form w(x)
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Chapter 35 Solutions
Physics for Scientists and Engineers, Vol. 1
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- Q Calculate the velocity of longitudinal and shear elastic waves in a cubical crystal along (111) dire tion.arrow_forwardGiven an infinite well of length 0 to L, and an initial wavefunction which is atent shaped (triangle) with a value rising from zero at x=0 tosome maximum value at x=L/2 (midpoint) and then descending withequal, but opposite slope back to zero at x=L. The slope is positive a when0 < x < L/2 and negative a when L/2 < x < L. (A) write an equation (or more if you need to) for the wavefunction with a single normalization constant,A. (B) find A via normalization. (C) find the probability of a measurement of energy finding the value of the ground state energy. (D) find the probability of a measurement of energy finding the value of the first excidedstate energy. These eigenenergies are those of the infinite well,and you’ll need the corresponding eigenfunctions.arrow_forwardIn the region 0 < x < a, a particle is described by the wave function y₁(x) = -b(x² - a²). In the region a≤ x ≤w, its wave function is y2(x) = (x-d)² - c. For x≥w, ¥3(x) = 0. (a) By applying the continuity conditions at x= a, find c and d in terms of a and b. (b) Find w in terms of a and b.arrow_forward
- A Free Particle moving with a wave fanction 4 = Ae -ix² e on a specified Path from o to och on the X axis Find the calibration constant.arrow_forwardThe amplitude of a scattered wave is given by 1 S(0) = (21 + 1)exp[id] sin 3i P(cos 0), l=0 where e is the angle of scattering, I is the angular momentum, ik is the incident momentum, and & is the phase shift produced by the central potential that is doing the scattering. The total cross section is oiot = S IS(O)²a2. Show that 47 Otot = FL(21+ 1)sin² § . %3D0arrow_forwardAt t = 0, the wavefunction is given as: p(x, t = 0) = bxe-ax on the domain 0 < x < ∞. (a) What is the average position of the particle? (b) What is the average linear momentum of the particle? (c) Calculate [f',p]Þ(x,0). Your answer should be explicit, including the details of (x, 0).arrow_forward
- if the wave function of a s ystem ucr) == (à) e: from the Periodr=othe r= infinite is a Cons tant magnitude , the mean dimension of this function is equalarrow_forwardA particle moving in one dimension has the wave function Y(x,t) = Aeli(ax-bt)] %3D where a and b are constants. What is the potential field V(x) in which the particle is moving?arrow_forwardThe harmonic oscillator Y, (x) wavefuction is given below. a) Use this function to calculate the average potential energy of an oscillating system. b) Show that the average potential energy is half of the total energy of this system. v,(x) = ()* (4q³\1/4 xe-ax? /2 where a = Jkµ /ħarrow_forward
- In the region 0 w, V3 (x) = 0. (a) By applying the continuity conditions atx = a, find c and d in terms of a and b. (b) Find w in terms of a and b. -arrow_forwardUsing the linearized theory, calculate the lift and wave-drag coefficients for an infinitely thin flat plate in a Mach 2.6 freestream at angles of attack of(a) α = 5◦ (b) α = 15◦ (c) α = 30◦Compare these approximate results with those from the exact shockexpansion theory. What can you conclude about the accuracy of linearized theory in this case?arrow_forwardA free particle moving along positive x-axis encounter three regions as shown in the figure. The wave functions of the particle in region 1 and region 2 are of the form 4(x) = Asin(kx- wt). Where k=2T/A is a wave number and wt = o is the phase term. In region 1, the amplitude of the wave function A1=11.5, wavelength A1 = 4.97 nm and phase = -65.3°. The wavelength in region 2 is A2 = 10.5 nm. The boundary C is located at x = 0, and the boundary D is located at x = L, where L = 20 nm. Using the mathematical features of wave function, find the amplitude of the wave function and the phase in region 2. (A2 and ø2) Region 1 Region 2 Region 3 C D (x= 0) (x = L)arrow_forward
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