Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Question
Chapter 7, Problem 6Q
To determine
The suitability of portraying wave functions and potential barriers on the same graph and discuss whether a wave whose crest falls below the top of square barrier ever penetrate the barrier.
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Determine the normalization constant for the wavefunction for a 3-dimensional box (3 separate infinite 1-dimensional wells) of lengths a (x direction), b (y direction), and c (z direction).
If the walls of a potential energy well have finite height, V0, the wave function that describes the particle inside the box does not vanish on the walls, but continues through the barrier power. Discuss, only conceptually, the diagrams drawn below for the three first energy levels. It is not to make a treatise about it, especially copied from books. It's simply to explain how much you understand about the concepts linked to graphics below.
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V (x):
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difference in this context means that you should enter your final result as a positive number).
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- A. at pattern. Let's ssuming that the e angular spatial poral frequencies w, correspond to e is then W, 1) ir) [7.33] avelength of the quals the group eing amplitude- e waves of fre- of modulating and sum over is called the wer sideband. 7.19 Given the dispersion relation w = ak', compute both the phase and group velocities. -7.20* Using the relation 1/v = dk/dv. prove that 1 Vg I V₂ 7.21* In the case of lightwaves, show that V = 1 Ve v dv v² dv V 7.22 The speed of propagation of a surface wave in a liquid of depth much greater than λ is given by v dn c dv 11 -+- C solve 7.25 only where g = acceleration of gravity, λ = wavelength, p = density. Y = surface tension. Compute the group velocity of a pulse in the long wavelength limit (these are called gravity waves). 7.23* Show that the group velocity can be written as dv dλ 7.24 Show that the group velocity can be written as gλ 2πΥ + 2πT pλ Vg = V-A ( n + w(dn/dw) 7.25 With the previous problem in mind prove that dn (v) dv n₂ = n(v) + v.…arrow_forwardConsider a particle in a box of length L with one end coinciding with the origin. Consider the state with n=2. 1. Compute the expectation value of position as a function of time 2. As well as the extrema in the probability density as a function of time. Interpret.arrow_forwardWhy don't you include the time dependent part of the wave equation when finding the expectation value of the potential? I don't see how the modulus of the wave function gets rid of the time dependent part. Can you please explain?arrow_forward
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