Question

Consider a two-dimensional state vector space and a basis in this space lay), laz), eigenvectors of an observable A: A|az) = ajlaj) Alaz) = azlaz) A representation of Hamiltonian operator in this basis is: h = (9) - Calculate the dispersion of measurements of A and Hat time t. Is the uncertainty principle Energy x Time fulfilled?

Answer 1

Jems with Solution 12 We can write he basis vectores es lineare combination of the both live I last I lazy where i wred the paopendy of sonnalization Given Ala) & A, las) and Ala27 - Azlan) First dispension of measurements of A, which is Vaniance of 2nte = 1.21 ) (3 x 10 x2x2x 24 -4.5 Jlev a bed (H A. (E+E 0 At time t, the ens can be Dritter och - byt tion to en rder. 4th 192) ( : 4 (16)= 48 h to the e † 19) + it best 2 Az 14192) Ooit then (A) xel 2. -28 Az 2 ور 2 to firs Similarly, <A> 2 2 Then 2 US 4. 4. 9 {a, Ala) tt & t. e 5 at 1(a, +42) (ohen two teams Canelled because say) and (az) are, I (2 ta) oathogonal to each other 4A = Vans - Vă (2,040,2) - ( (0,1443 +29,04)) A2 –Ragar Ś Cay-ay), 04.(09) 44, -an) So dispension of A, DA 12 Caran) Ore (AA) - Cap-an) H-LOJ 18 Now task is to find out eigen value and commesponeling ergens vectons. H-RI) = 0 => 1 -=0 0 ) 2 2822) Eigen vector of eigenvalue to 15-0) > ny Klencie, p. 4 (1) Now De 20 en s
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