An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter A.2, Problem 10P
To determine
To Draw: the wave function for which the product
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A real wave function is defined on the half-axis:
[0≤x≤00) as y(x) = A(x/xo)e-x/xo
where xo is a given constant with the dimension of length.
a) Plot this function in the dimensionless variables and find the constant A.
b) Present the normalized wave function in the dimensional variables.
Hint: introduce the dimensionless variables = x/xo and Y(5) = Y(5)/A.
A certain wavefunction is zero everywhere except between x = 0 and x = L. where it has the constant value A. Normalize the wavefunction.
Given 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.
Chapter A Solutions
An Introduction to Thermal Physics
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