A system that is measured to be in a state |ni cannot simultaneously
... A system that is measured to be in a state |ni cannot simultaneously be measured to be in an orthogonal state |mi. The probabilities sum to unity because the system must be in some state. Since the density operator ⇢ is hermitian, it has a complete, orthonormal set of eigenvectors |ki all of which h ...
... A system that is measured to be in a state |ni cannot simultaneously be measured to be in an orthogonal state |mi. The probabilities sum to unity because the system must be in some state. Since the density operator ⇢ is hermitian, it has a complete, orthonormal set of eigenvectors |ki all of which h ...
Vector fields and differential forms
... There is a more general concept of a manifold. The idea is that near each point the manifold looks like an open ball in Rn , but on a large scale it may have a different geometry. An example where n = 1 is a circle. Near every point one can pick a smooth coordinate, the angle measured from that poin ...
... There is a more general concept of a manifold. The idea is that near each point the manifold looks like an open ball in Rn , but on a large scale it may have a different geometry. An example where n = 1 is a circle. Near every point one can pick a smooth coordinate, the angle measured from that poin ...
