PJAstro

Dear Absolute,

I found an earlier discussion on your site about Dirac's bra-ket notation that was very useful. My question now is, for "simple" quantum systems, where finite-dimensional vectors spaces might be adequate in place of Hilbert spaces, are there examples of worked problems that involve the actual vector entries, given some basis? For example, a quantum state might involve 1 electron or other particle, with a position, velocity, angular momentum, spin, charge, etc. Does the ket-vector used to represent this state in some ket-space with a basis have entries corresponding to these variables? Like a vector |v> = (x,y,z,velocity,angularmomentum,...)? I can visualize how a complex "state of the system" might benefit from an infinite sequence of these values, but I'm not clear on what the entries represent. Thanks for any insight!

PJAstro

I found an earlier discussion on your site about Dirac's bra-ket notation that was very useful. My question now is, for "simple" quantum systems, where finite-dimensional vectors spaces might be adequate in place of Hilbert spaces, are there examples of worked problems that involve the actual vector entries, given some basis? For example, a quantum state might involve 1 electron or other particle, with a position, velocity, angular momentum, spin, charge, etc. Does the ket-vector used to represent this state in some ket-space with a basis have entries corresponding to these variables? Like a vector |v> = (x,y,z,velocity,angularmomentum,...)? I can visualize how a complex "state of the system" might benefit from an infinite sequence of these values, but I'm not clear on what the entries represent. Thanks for any insight!

PJAstro