Notes on Quantum Mechanics - Department of Mathematics
... operator D is not — in fact, we saw in class that the integration by parts formula implies that D is skew-adjoint, meaning D∗ = −D. However, for any skew-adjoint operator, multiplication by i gives a self-adjoint operator, so iD is self-adjoint. Hence in reality, the speed operator should be iD and ...
... operator D is not — in fact, we saw in class that the integration by parts formula implies that D is skew-adjoint, meaning D∗ = −D. However, for any skew-adjoint operator, multiplication by i gives a self-adjoint operator, so iD is self-adjoint. Hence in reality, the speed operator should be iD and ...
Cross Products next
... –F; what is the total to torque on the two particles measured at the origin? b) Two particles at positions r= (1,1,0) mm and –r are acted on by forces F = (1,-1,0) N and F; what is the total to torque on the two particles measured at the origin? ...
... –F; what is the total to torque on the two particles measured at the origin? b) Two particles at positions r= (1,1,0) mm and –r are acted on by forces F = (1,-1,0) N and F; what is the total to torque on the two particles measured at the origin? ...
Vector length bound
... Suppose in contradiction, there is a way to implement vector clocks with k-vectors of reals, where k < n. By Claim 1, ai+1 || bi => V(ai+1) and V(bi) are incomparable => V(ai+1) is larger than V(bi) in some coordinate h(i) => h : {0,…,n-1} {0,…,k-1} ...
... Suppose in contradiction, there is a way to implement vector clocks with k-vectors of reals, where k < n. By Claim 1, ai+1 || bi => V(ai+1) and V(bi) are incomparable => V(ai+1) is larger than V(bi) in some coordinate h(i) => h : {0,…,n-1} {0,…,k-1} ...
