Question 1: Create a state vector representing the state below: 42 cells hidden 126) = √2 PO") + √/2₂P 1") Question 2: S

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Question 1 Create A State Vector Representing The State Below 42 Cells Hidden 126 2 Po 2 P 1 Question 2 S 1 (88.27 KiB) Viewed 12 times

Question 1: Create a state vector representing the state below: 42 cells hidden 126) = √2 PO") + √/2₂P 1") Question 2: Show that this vector is properly normalized. You'll need to take the adjoint of ) to find the bra ( and then multiply the two vectors together to show: (22) = 1 I know you don't need to take the conjugate since this has all real coefficient, but doing this will make it easier to copy/paste code for later. [ ] 42 cells hidden Question 3: The following state vector is not normalized (i.e the "overlap" of this state vector with itself is not 100% ) . $$\lvert \phi \rangle = 3 \lvert "0" \rangle + 5 \lvert "1"\rangle Calculate the normalization constant C such that o) is normalized. Check your results using your technique in problem 2 above to show the new state vector has 100% overlap with itself. Hint: You'll want to define a constant like C_squared such that (16) = C². Next take the square root of this number (maybe naming it C) and use the fact that your normalized vector will be lp') = 6). I usually name this new vector something like phi_prime Hint: You can reuse your code from the previous question to check that the resulting vector is normalized [ ] 41 cell hidden ▸ Question 4 The following state vector is clearly not normalized. Find the normalization constant and then show the resulting state vector is normalized. |) = 21" 0") +8i|" 1 ") Hint: Remember that i in Python is 1j. You can write 8i as 8j.