Suppose that the wave function for a microscopic state [represented by the wave function (x)] can be written as 2-√2i 3 - 4₁(x) + 1 + √2i 3 -4₂(x) 4(x) = 2-√2i 1+√zi Where ₁(x) and ₂(x) are a set of orthonormal eigenfunctions of an identical energy operator. are Fourier coefficient constant for ₁(x) and ₂(x), respectively. The eigenvalues of ₁(x) and ₂(x) are 4E and 6E, respectively. and 3 3 (a) Verify that the wave function (x) is normalized. (b) Express the average value of energy, , of the energy operator in terms of E.
Suppose that the wave function for a microscopic state [represented by the wave function (x)] can be written as 2-√2i 3 - 4₁(x) + 1 + √2i 3 -4₂(x) 4(x) = 2-√2i 1+√zi Where ₁(x) and ₂(x) are a set of orthonormal eigenfunctions of an identical energy operator. are Fourier coefficient constant for ₁(x) and ₂(x), respectively. The eigenvalues of ₁(x) and ₂(x) are 4E and 6E, respectively. and 3 3 (a) Verify that the wave function (x) is normalized. (b) Express the average value of energy, , of the energy operator in terms of E.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
solve parts a and b
![Suppose that the wave function for a microscopic state [represented by the wave function
(x)] can be written as
2-√2i
3
4(x) =
1 + √2i
3
Where ₁(x) and ₂(x) are a set of orthonormal eigenfunctions of an identical energy operator.
and are Fourier coefficient constant for ₁(x) and ₂(x), respectively. The
2-√2i
1+√2i
3
3
eigenvalues of ₁(x) and ₂(x) are 4E and 6E, respectively.
(a) Verify that the wave function (x) is normalized.
(b) Express the average value of energy, <E>, of the energy operator in terms of E.
-4₁(x) +
-4₂(x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6957468-6fb1-4659-9083-987b06676d6d%2F79a216ac-37e0-44d1-82d5-3296b45a14df%2Fhgvicag_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that the wave function for a microscopic state [represented by the wave function
(x)] can be written as
2-√2i
3
4(x) =
1 + √2i
3
Where ₁(x) and ₂(x) are a set of orthonormal eigenfunctions of an identical energy operator.
and are Fourier coefficient constant for ₁(x) and ₂(x), respectively. The
2-√2i
1+√2i
3
3
eigenvalues of ₁(x) and ₂(x) are 4E and 6E, respectively.
(a) Verify that the wave function (x) is normalized.
(b) Express the average value of energy, <E>, of the energy operator in terms of E.
-4₁(x) +
-4₂(x)
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