Linear Transformations and Group
... What are the eigenvectors and eigenvalues of DT ? Let’s find the vectors v that are simultaneous eigenvectors of all the DT ’s. First, observe that DS ( DT v ) (t ) = v (t + T + S ) = DT +S ( v ) , so that DS DT = DT +S . Intuitively, translating in time by T, and then by S, is the same as translati ...
... What are the eigenvectors and eigenvalues of DT ? Let’s find the vectors v that are simultaneous eigenvectors of all the DT ’s. First, observe that DS ( DT v ) (t ) = v (t + T + S ) = DT +S ( v ) , so that DS DT = DT +S . Intuitively, translating in time by T, and then by S, is the same as translati ...
Homework 9 - Solutions
... and on the right by S −1 we get SBS −1 = S(S −1 AS)S −1 = (SS −1 )A(SS −1 ) = IAI = A. Since A = SBS −1 = (S −1 )−1 BS −1 , A is similar to B. (iii) Write C = T −1 BT and B = S −1 AS for invertible matrices S, T . Then C = T −1 BT = T −1 (S −1 AS)T = (T −1 S −1 )A(ST ) = (ST )−1 A(ST ) Therefore C i ...
... and on the right by S −1 we get SBS −1 = S(S −1 AS)S −1 = (SS −1 )A(SS −1 ) = IAI = A. Since A = SBS −1 = (S −1 )−1 BS −1 , A is similar to B. (iii) Write C = T −1 BT and B = S −1 AS for invertible matrices S, T . Then C = T −1 BT = T −1 (S −1 AS)T = (T −1 S −1 )A(ST ) = (ST )−1 A(ST ) Therefore C i ...
What Have I Learned From Physicists / Computer Scientists
... about continuous-time quantum computing… • Suppose a Hamiltonian H has the form iHi, where each Hi acts on two neighboring vertices of a graph. Can we approximate eiH by a unitary whose only nonzero entries are between neighboring vertices? What about ...
... about continuous-time quantum computing… • Suppose a Hamiltonian H has the form iHi, where each Hi acts on two neighboring vertices of a graph. Can we approximate eiH by a unitary whose only nonzero entries are between neighboring vertices? What about ...
PHYS3111, 3d year Quantum Mechanics General Info
... For the third tutorial I recommend problems 26,27,32. Problem 29 is in assignment, so it is excluded from the tutorial. I would like to comment on the 3 following topics (i) Operators (ii) Dirac notations (iii) Solution of time dependent Schrodinger Eq. These are 2nd year quantum mechanics topics, b ...
... For the third tutorial I recommend problems 26,27,32. Problem 29 is in assignment, so it is excluded from the tutorial. I would like to comment on the 3 following topics (i) Operators (ii) Dirac notations (iii) Solution of time dependent Schrodinger Eq. These are 2nd year quantum mechanics topics, b ...
