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A spin-particle is in the spin state |A), described by the ket 7 |A) = 5√₂ tu) +5√₂ tu). I (a) Verify that A) is normalised. (b) Using the spinor representation -8-8-8 14₂) = 8 | tv)=√· += √2]· ts) = 11 find the values of c₁ and c₂ for which |A) = C₁1|1₂) + C₂+₂). (c) If the observable S, is measured in the spin state |A), what values can be obtained and what are their probabilities? (d) Find the expectation value of S, in the spin state 4). (e) With reference to the properties of angular momentum, explain briefly how the results of the Stern-Gerlach experiment provide evidence of the existence of spin.

A spin-particle is in the spin state |A), described by the ket 7 |A) = 5√₂ tu) +5√₂ tu). I (a) Verify that A) is normalised. (b) Using the spinor representation -8-8-8 14₂) = 8 | tv)=√· += √2]· ts) = 11 find the values of c₁ and c₂ for which |A) = C₁1|1₂) + C₂+₂). (c) If the observable S, is measured in the spin state |A), what values can be obtained and what are their probabilities? (d) Find the expectation value of S, in the spin state 4). (e) With reference to the properties of angular momentum, explain briefly how the results of the Stern-Gerlach experiment provide evidence of the existence of spin.

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A spin-particle is in the spin state |A), described by the ket 7 i |4) = 5√2 tu) +5√2 tu). (a) Verify that A) is normalised. (b) Using the spinor representation (+₂) = ₁ | +) = √/2₁ 11³) = ₁ 1 +2) = [8] find the values of c₁ and c₂ for which |A) = C₁|1₂) + C₂l+₂). (c) If the observable S₂ is measured in the spin state |A), what values can be obtained and what are their probabilities? (d) Find the expectation value of S₂ in the spin state [A). (e) With reference to the properties of angular momentum, explain briefly how the results of the Stern-Gerlach experiment provide evidence of the existence of spin.
Transcribed Image Text:A spin-particle is in the spin state |A), described by the ket 7 i |4) = 5√2 tu) +5√2 tu). (a) Verify that A) is normalised. (b) Using the spinor representation (+₂) = ₁ | +) = √/2₁ 11³) = ₁ 1 +2) = [8] find the values of c₁ and c₂ for which |A) = C₁|1₂) + C₂l+₂). (c) If the observable S₂ is measured in the spin state |A), what values can be obtained and what are their probabilities? (d) Find the expectation value of S₂ in the spin state [A). (e) With reference to the properties of angular momentum, explain briefly how the results of the Stern-Gerlach experiment provide evidence of the existence of spin.
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