0

The inner product $\langle\phi|\psi\rangle$ of two state vectors in the Hilbert space can be thought of as the generalization of the ordinary dot product $\vec{A}\cdot{\vec B}$ of two vectors in 3D space. This is an appropriate generalization in the sense that for ${\vec A}=\vec{B}$, the dot product gives the norm square of ${\vec A}$ and similarly for $\phi=\psi$ we get norm square of $\phi$.

Does the ordinary cross-product ${\vec A}\times {\vec B}$ of two vectors in 3D have any generalization in quantum mechanics? Thanks.

Solidification
  • 713
  • 1
    Related: 1 , 2, 3 – Anindya Prithvi Nov 02 '20 at 03:54
  • The answer is obviously "no!!", but how do you prove it? The cross product is problematic to generalize usefully for anything but 2-vectors, as you see in the linked questions, and the generalizations become pointless for the infinite-dimensional vectors of QM. What's your point? – Cosmas Zachos Nov 19 '20 at 16:48

0 Answers0