The group SU (2) is the group of special unitary (2 x 2) matrices, i.e., the unitary (2 x 2) matrices with determinant 1. A representation of the elements of SU (2) is Û (ã) = exp(- 1 ã. 5) where a; h α; € R, j = 1,2,3 and Ŝ= is the spin operator which is proportional to the vector of Pauli matrices 3 = (₁, 62, 63)¹ 6₁ = (₁1)₁ 6₂ = (1¹) and 63 = (1-₁) G 0 a. Write [Û (a)] as a linear combination of 2 × 2 Pauli matrices to show that Û (a) = cos 1₂ - i sin 2.8
The group SU (2) is the group of special unitary (2 x 2) matrices, i.e., the unitary (2 x 2) matrices with determinant 1. A representation of the elements of SU (2) is Û (ã) = exp(- 1 ã. 5) where a; h α; € R, j = 1,2,3 and Ŝ= is the spin operator which is proportional to the vector of Pauli matrices 3 = (₁, 62, 63)¹ 6₁ = (₁1)₁ 6₂ = (1¹) and 63 = (1-₁) G 0 a. Write [Û (a)] as a linear combination of 2 × 2 Pauli matrices to show that Û (a) = cos 1₂ - i sin 2.8
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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![1. The group SU (2) is the group of special unitary (2 x 2) matrices,
i.e., the unitary (2 x 2) matrices with determinant 1. A
representation of the elements of SU (2) is Û (a) = exp(-ã.5)
where a Ŝ
€ R, j = 1,2,3 and 3 = is the spin operator which is
proportional to the vector of Pauli matrices & = (₁, 6₂, 63)¹
02,
o
0
1 and 63 = (1₁)
0
2₁ = (₁ 2)₁ 6₂ = (₁ 3²1)
1),
¹) and
1
0
a. Write [Û (a)] as a linear combination of 2 × 2 Pauli matrices to
show that Û (a) = cos ½ – i sin ªª. ☎
22](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe44e7fdc-f850-4dc9-8247-4240983c667e%2Fcf010176-28b7-4f95-a5cf-97153fec63c4%2Fpol9sq_processed.png&w=3840&q=75)
Transcribed Image Text:1. The group SU (2) is the group of special unitary (2 x 2) matrices,
i.e., the unitary (2 x 2) matrices with determinant 1. A
representation of the elements of SU (2) is Û (a) = exp(-ã.5)
where a Ŝ
€ R, j = 1,2,3 and 3 = is the spin operator which is
proportional to the vector of Pauli matrices & = (₁, 6₂, 63)¹
02,
o
0
1 and 63 = (1₁)
0
2₁ = (₁ 2)₁ 6₂ = (₁ 3²1)
1),
¹) and
1
0
a. Write [Û (a)] as a linear combination of 2 × 2 Pauli matrices to
show that Û (a) = cos ½ – i sin ªª. ☎
22
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