LQ31 - Name:__________________________________________

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Unformatted text preview: Name:__________________________________________ Date:__________________________ PHYS 360 Lecture Question #31 X-Splitter An unpolarized beam of spin ½ Sz +z particles is travelling in the +y direction. A Stern ­Gerlach apparatus Sx is aligned to split this beam into spin Z-Splitter up (+½) and spin down ( ­½) beams; we call this a Z ­Splitter. Since the +y incident beam was unpolarized, the two new beams have equal numbers. +x The spin down beam is blocked, and the spin up beam enters an X ­Splitter (a Stern ­ Gerlach apparatus aligned in the x ­direction), which produces two new beams. 1.What are the possible spin components of these two beams? (Specify Sx, Sy, and/or Sz values.) 2.Do they have equal numbers of particles, or does one beam have all the particles? S Z-Splitter !"#$%&%"'()*+,)%-" "1% z !+ = $ ' , # 0& " 0% z !( = $ ' #1& ."#$%&%"'()*+,)%-" " $ ( !+ ) = $ $ $ # x 1% ' 2' , 1' ' 2& " $ ( !( ) = $ $ $ # x 1% ' 2' (1 ' ' 2& /0$)%',01$+,)-" ( !+ ) = x 1 2 {! z + z + !" , } ( !" ) = x 1 2 {! z + z " !" } 23)30$4"5$63"'()*+,)-" # a + b& x # a " b& x z z ! = a! + + b! " = % !+ !, $ 2( + % 2( " ' $ ' normalization: a + b = 1 2 2 78" ...
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