Fund Quantum Mechanics Lect & HW Solutions 84

Fund Quantum Mechanics Lect & HW Solutions 84 -...

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66 CHAPTER 5. MULTIPLE-PARTICLE SYSTEMS If this is plugged into the expression for the solution, c 1 ψ 1 + c 2 ψ 2 , it takes the form ¯ c 1 ¯ ψ 1 + ¯ c 2 ¯ ψ 2 where ¯ c 1 = c 1 + εc 2 α (1 ε 2 ) ¯ c 2 = c 2 + εc 1 α (1 ε 2 ) . So, while the constants ¯ c 1 and ¯ c 2 are diFerent from c 1 and c 2 , the same solution can be found equally well in terms of ¯ ψ 1 and ¯ ψ 2 as in terms of ψ 1 and ψ 2 . In the terms of linear algebra, ¯ ψ 1 and ¯ ψ 2 “span the same function space” as ψ 1 and ψ 2 : any wave function that can be described as a combination of ψ 1 and ψ 2 can also be described in terms of ¯ ψ 1 and ¯ ψ 2 , although with diFerent constants. This is true as long as the de±nitions of the new functions can be solved for the old functions as above. The matrix of coe²cients,
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Unformatted text preview: here p P must have a nonzero determinant. 5.4 Spin 5.4.1 Solution spin-a Question: Delta particles have spin 3 / 2 . What values can their spin angular momentum in a given direction have? Answer: 3 2 h, 1 2 h, 1 2 h, 3 2 h. Reread the text if you got this wrong, because spin is really, really, important in quantum mechanics. 5.4.2 Solution spin-b Question: Delta particles have spin 3 / 2 . What is their square spin angular momentum?...
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