For the Pauli spin matrix A in Problem 6, find the matrices sin kA, cos kA, ekA, and etkA where i = V-1.
For the Pauli spin matrix A in Problem 6, find the matrices sin kA, cos kA, ekA, and etkA where i = V-1.
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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![**6. Pauli Spin Matrices in Quantum Mechanics**
The Pauli spin matrices are fundamental in quantum mechanics and are represented as follows:
**Matrix A:**
\[
A = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}
\]
**Matrix B:**
\[
B = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}
\]
**Matrix C:**
\[
C = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}
\]
These matrices are used to describe the spin of 1/2 particles, such as electrons, in quantum mechanics. Each matrix corresponds to spin measurements along different axes in three-dimensional space: x, y, and z, respectively. They serve as the basis for describing spin operators in the formalism of quantum mechanics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b6d687b-9b3f-47af-8b4d-c251df44093c%2F2793833e-7490-4211-9700-66f1e0e984fe%2Faqbp0xh_processed.png&w=3840&q=75)
Transcribed Image Text:**6. Pauli Spin Matrices in Quantum Mechanics**
The Pauli spin matrices are fundamental in quantum mechanics and are represented as follows:
**Matrix A:**
\[
A = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}
\]
**Matrix B:**
\[
B = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}
\]
**Matrix C:**
\[
C = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}
\]
These matrices are used to describe the spin of 1/2 particles, such as electrons, in quantum mechanics. Each matrix corresponds to spin measurements along different axes in three-dimensional space: x, y, and z, respectively. They serve as the basis for describing spin operators in the formalism of quantum mechanics.
Transcribed Image Text:For the Pauli spin matrix \( A \) in Problem 6, find the matrices \(\sin kA\), \(\cos kA\), \(e^{kA}\), and \(e^{ikA}\) where \(i = \sqrt{-1}\).
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