You are given in each case one period of a function. Sketchseveral periods of the function and expand it in a sine-cosineFourier series, and in a complex exponential Fourier series.
a) f(x) = e^x, -Ï<x<Ï;

b) f(x) = e^x, 0<x<Ï

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consider an ensamble of classical one-dim harmonicoscillators.

let the displacement x of an oscillator as a function of time tbe given by x=Acos(wt+ï»¿ï»¿Î¸). Assume that the phase angle Î¸ isequally likely to assume any value in its range 0<ï»¿ï»¿Î¸<2Ï. Theprobability w(Î¸)dÎ¸ that Î¸ lies in the range between Î¸ and Î¸ + dÎ¸ isthen simply w(Î¸)dÎ¸ = (2Ï)^-1dÎ¸. For any fixed time t, find theprobability P(x)dx that s lies between x and x+dx by summing w(Î¸)dÎ¸over all angles Î¸ for which x lies in this range. Express P(x) interms of A and x.

A particle of mass m is bound in a finite one-dimensional squarewell described by the potential energy function: V(x)=0 for x<a(region I)
=-v0 for -a<=x<=a (region II) with v0>0
=0 for x>a (region III)
The energy of the particle has some definite negative value-v0<E1<0.
Consider the time independent Schrodinger equation.
Question: In each of the three regions write the normalizablespatial wave function f(x) of the particle assuming that f is aneven function of x, i.e. f(x)=f(-x) and calculate the constants inyour function that are determined by the given quantities.

There is a square barrier that has the following wavefunctions:

Ï1 = Ae^(-ikx) + Be^(ikx) for (-â < x < 0)

Ï2 = Ccos(lx) + Dsin(lx) for (0 < x < a)

Ï3 = Fe^(ikx) for (a < x < â)

and their is a potential of:

V(x) = Vo for 0 < x < a

and

0 otherwise

E > 0 so the stat is scattering.

Answer the following questions:

1. Apply any essential boundary conditions at x = 0. Whensetting these boundary conditions you can neglect the wavereflected at the boundary of x = a. Show these boundaries.

2. Now set the boundary conditions for x = a. You must accountfor the neglected wave durning the first question here.

3. Using the answers from questions 1 and 2 show thattransmission should be:

T = (16E (Vo-E)/Vo^2) e^-2ka

Make sure you identify what k is in the above equation.

I am posting this question however I can only offer 175 karmapoints per a question. If you answer this question in detail, Iwill also be posting two other 175 points that say please answerthis question. If you answer this question and simply answer theother two with the response 'It is answered" I will give you all525 points! Thanks!

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You are given in each case one period of a function. Sketchseveral periods of the function and expand it in a sine-cosineFourier series, and in a complex exponential Fourier series.
a) f(x) = e^x, -Ï<x<Ï;

b) f(x) = e^x, 0<x<Ï

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Physics: Principles with Applications

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You are given in each case one period of a function. Sketchseveral periods of the function and expand it in a sine-cosineFourier series, and in a complex exponential Fourier series.a) f(x) = ex, -Ï<x<Ï; b) f(x) = ex, 0<x<Ï

Related textbook solutions

Physics: Principles with Applications

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You are given in each case one period of a function. Sketchseveral periods of the function and expand it in a sine-cosineFourier series, and in a complex exponential Fourier series.
a) f(x) = e^x, -Ï<x<Ï;

b) f(x) = e^x, 0<x<Ï