Consider the entangled wave function for two photons, Assume that the polarization operator P Euml i has the properties P Euml Iuml i i (H) Iuml i (H) and P Euml i Iuml i (V ) Iuml i (V ), where i 1 or i 2 H and V designate horizontal and vertical polarization, respectively a Show that Iuml 12 is not an eigenfunction of P Euml 1 or P Euml 2 b Show that each of the two terms in Iuml 12 is an eigenfunction of the polarization operator P Euml 1 c What is the average value of the polarization P 1 that you will measure on identically prepared systems (,(H)w,(V) (V)w2(H)) V12

Question: Consider the entangled wave function for two photons, Assume that the polarization operator PË i has the properties PËÏ i i (H) = Ï i

Consider the entangled wave function for two photons,

-(,(H)w,(V) + ¥¼(V)w2(H)) V12 =

Assume that the polarization operator PË†_i has the properties PË†Ïˆ_i i (H) = ˆ’Ïˆ _i (H) and PË†_iÏˆ i (V ) = + Ïˆ _i (V ), where i = 1 or i = 2. H and V designate horizontal and vertical polarization, respectively.

a. Show that Ïˆ₁₂ is not an eigenfunction of PË†₁ or PË†₂.

b. Show that each of the two terms in Ïˆ₁₂ is an eigenfunction of the polarization operator PË†₁.

c. What is the average value of the polarization P₁ that you will measure on identically prepared systems?

-(,(H)w,(V) + (V)w2(H)) V12 =

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