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Question: 3 a a particle orbits a fixed point in space...

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3. (a) A particle orbits a fixed point in space. Given that L-=-ih- , find the eigenvalues аф and normalised eigenfunctions of the z-component of the particles angular momentum. (5 marks) Explain clearly your reasoning at each important step An electron is in the spin state x)-A G) Normalise x) and hence determine the constant A (ii) If you measured the z-component of the electrons spin, s, . what values could (b) in the usual s basis you get and what is the probability of obtaining each? What is the expectation value of s,? (iii) If, instead, you measured the x-component of the electrons spin, s, , what values could you get and what is the probability of obtaining each? expectation value of s,? What is the The Pauli Matrices are: σ,- 5 marks)

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