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Problem 4.53 Work out the spin matrices for arbitrary spin s, generalizing spin (1)/(2) (Equations 4.145 and 4.147), spin 1 (Problem 4.31), and spin 3/2 (Problem 4.52). Answer: S_(z)=ℏ([s,0,0,...,0 0,s-1,0,...,0 0,0,s-2,...,0 ..., ..., ..., ..., ... 0,0,0,...,-s]) S_(x)=(ℏ)/(2)([0,b_(s),0,0,...,0,0 b_(s),0,b_(s-1),0,...,0,0 0,b_(s-1),0,b_(s-2),...,0,0 0,0,b_(s-2),0,...,0,0 ..., ..., ..., ..., ..., ..., ... 0,0,0,0,...,0,b_(-s+1) 0,0,0,0,...,b_(-s+1),0]) S_(y)=(ℏ)/(2)([0,-ib_(s),0,0,...,0,0 ib_(s),0,-ib_(s-1),0,...,0,0 0,ib_(s-1),0,-ib_(s-2),...,0,0 0,0,ib_(s-2),0,...,0,0 ..., ..., ..., ..., ..., ..., ... 0,0,0,0,...,0,-ib_(-s+1) 0,0,0,0,...,ib_(-s+1),0]) where b_(j)=√((s+j)(s+1-j)). Book: Introduction to Quantum Mechanics 2nd Edition (Griffiths)

Name: problem 453 work out the spin matrices for arbitrary spin s generalizing spin 12 equations 4145 and 4147 spin 1 problem 431 and spin 32 problem 452 answer szs000 0s 100 00s 20 000 s sx20b 73125
Uploaded: 2023-08-19T19:21:43-08:00
Channel: Victor Salazar
Description: problem 453 work out the spin matrices for arbitrary spin s generalizing spin 12 equations 4145 and 4147 spin 1 problem 431 and spin 32 problem 452 answer szs000 0s 100 00s 20 000 s sx20b 73125

          Problem 4.53 Work out the spin matrices for arbitrary spin s, generalizing spin (1)/(2) (Equations 4.145 and 4.147), spin 1 (Problem 4.31), and spin 3/2 (Problem 4.52).
Answer:
S_(z)=ℏ([s,0,0,...,0
0,s-1,0,...,0
0,0,s-2,...,0
..., ..., ..., ..., ...
0,0,0,...,-s])
S_(x)=(ℏ)/(2)([0,b_(s),0,0,...,0,0
b_(s),0,b_(s-1),0,...,0,0
0,b_(s-1),0,b_(s-2),...,0,0
0,0,b_(s-2),0,...,0,0
..., ..., ..., ..., ..., ..., ...
0,0,0,0,...,0,b_(-s+1)
0,0,0,0,...,b_(-s+1),0])
S_(y)=(ℏ)/(2)([0,-ib_(s),0,0,...,0,0
ib_(s),0,-ib_(s-1),0,...,0,0
0,ib_(s-1),0,-ib_(s-2),...,0,0
0,0,ib_(s-2),0,...,0,0
..., ..., ..., ..., ..., ..., ...
0,0,0,0,...,0,-ib_(-s+1)
0,0,0,0,...,ib_(-s+1),0])
where
b_(j)=√((s+j)(s+1-j)).
Book: Introduction to Quantum Mechanics 2nd Edition (Griffiths)

problem 453 work out the spin matrices for arbitrary spin s generalizing spin 12 equations 4145 and 4147 spin 1 problem 431 and spin 32 problem 452 answer szs000 0s 100 00s 20 000 s sx20b 73125

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