Daily_013.SOLN - 2011 E. Szarmes PHYS 274 Q6S.2 DAILY...

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© 2011 E. Szarmes PHYS 274 DAILY ASSIGNMENT 13 — DUE WEDNESDAY, FEB 16/11 PROF. SZARMES Q6S.2 According to the superposition principle, the electrons in the recombined beam remain in the | +z spin state, but are expressed as a superposition of the | + ϑ〉 and | ϑ〉 states as follows: | +z = c 1 | + ϑ〉 + c 2 | ϑ〉 = ( + ϑ | +z ) | + ϑ〉 + ( ϑ | +z ) | ϑ〉 , and we wish to check that this is true. First we calculate the coefficients c 1 and c 2 , where c 1 = + ϑ | +z = ; c 2 = ϑ | +z = Next we substitute the expressions for | + ϑ〉 and | ϑ〉 , and we find that the superposition state is then which is indeed the | +z spin state. Q6S.3 If the electron energy is +E 0 in the | +x spin state and –E 0 in the | –x spin state then, by definition , these spin states are also energy eigenstates, since a definite energy is associated with each. The first step is to write the initial state | ψ (0) as a superposition of these energy eigenstates: | ψ (0) = = c 1 | +E 0 + c 2 | –E
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This note was uploaded on 03/07/2011 for the course PHYS 274 taught by Professor Ericszarmes during the Spring '11 term at University of Hawaii, Manoa.

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