Thus the matrix representation of S, is given by 0 √3 5,= + Sx (Ŝ+ + Ŝ_) · 1/² ħ 2 √30 02 0 0 0 2 0 √3 (0 0 √30) **** "N 3.24. A spin- particle is in the state 12/1) S- basis N 3 4i (a) Determine a value for N so that ) is appropriately normalized. (b) What is (S.) for this state? Suggestion: The matrix representation of S, is given in Example 3.4. (c) What is the probability that a measurement of S, will yield the value ħ/2 for this state?
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I need help with part c. I provided the matrix representation from example 3.4 for your reference.
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- 2 A.) FOR TWO OBSERVABLES A=x %3D B= LZ, FIND THE UNCERTAINTY RELATIONS TA Jo. AND B.) FOR THE STATE Ynim IN A HYOROGEN ATOM, FIND 8. USE THE DEFINITION OF STANDARD DEVIATION.TRQ. 3.1 Solve completely the following Quantum problem. Need full detailed answer, equations and if possible, theory/ literature. Question: A particle of spin 1 and a particle of spin 1/2 are in a configuration for which the total spin is equal to 1/2. If one were to measure the z-component of the spin of the particle with spin = 1, what values might one get and what are the probabilities associated with those values? Use Clebsch-Gordan table. Write the total spin state |s,ms> as linear combinations of |s1, ms1> |s2, ms2> states.A beam of spin-1/2 particles is prepared in the state 3 a. b. 14) = 5 |up spin S₂) + i |down spin S₂) √34 34 What would be the possible results of a measurement of the spin component S₂ and with what probabilities would they occur? ħ 2 Suppose that the S₂ measurement yields the result Sz Subsequent to that result, a second measurement is performed to measure the spin component Sx. What are the possible results of that measurement, and with what probabilities would they occur?
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