2. (a) Give an account of the concept of electron spin and outline how its existence was verified experimentally in the Stern-Gerlach experiment. The Pauli spin matrices may be written as: στ · = ( ) = ( ) 1 0 Oy and σz = 0 ( 6 -11) (b) Show that (}) and are eigenvectors of the operator Sy. Find the associated eigenvalues and normalisation constants. (c) Evaluate the expectation values (Sr), (Sy), (S2) and (S2) for a particle that has spin down in the y-direction. (d) A beam of spin-down particles, as determined by a Stern-Gerlach apparatus orientated in the y-direction, is passed through a Stern-Gerlach apparatus orientated in the z-direction. What are the probabilities of the possible results of the measurement of the spin along the direction of the x-axis?

2. (a) Give an account of the concept of electron spin and outline how its existence was verified experimentally in the Stern-Gerlach experiment. The Pauli spin matrices may be written as: στ · = ( ) = ( ) 1 0 Oy and σz = 0 ( 6 -11) (b) Show that (}) and are eigenvectors of the operator Sy. Find the associated eigenvalues and normalisation constants. (c) Evaluate the expectation values (Sr), (Sy), (S2) and (S2) for a particle that has spin down in the y-direction. (d) A beam of spin-down particles, as determined by a Stern-Gerlach apparatus orientated in the y-direction, is passed through a Stern-Gerlach apparatus orientated in the z-direction. What are the probabilities of the possible results of the measurement of the spin along the direction of the x-axis?

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.36P

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