Timeline for State of a system in Quantum Mechanics and state vectors
Current License: CC BY-SA 3.0
5 events
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| Sep 1, 2015 at 0:48 | comment | added | Prof. Legolasov | also a ray in the Hilbert space is a poor example of the representative, since the space of states is always a projective Hilbert space with a ray product defined on it. Therefore, rays and wavefunctions don't play the same role here. Instead, not wavefunctions, but the equivalence classes of wavefunctions with respect to an overall normalization constant should be considered rays (and hence represent states). I know you understand this, just emphasizing for @user1620696 because your answer does not make it clear enough IMHO. | |
| Sep 1, 2015 at 0:33 | comment | added | Prof. Legolasov | @user1620696 Hilbert spaces are considered isomorphic if there exists a one-to-one reversible linear map which preserves the Hilbert product. In this sense it really does not matter which representative objects we choose to describe the space of states; since all these choices are linked via linear maps that preserve the Hilbert structure, and the only observable things in QM are the modules-squared of the Hilbert products of different states. | |
| Aug 31, 2015 at 22:53 | comment | added | ACuriousMind♦ | @user1620696: Yes, when people use the bra-ket notation, they tend to not specify the Hilbert space more precisely than "space that is able to encode the information". (It is, however, assumed to be finite-dimensional or a separable space) | |
| Aug 31, 2015 at 22:49 | comment | added | Gold | Thanks for the answer. And in that case the a state vector (a ket) is simply an element of an appropriate Hilbert space which is able to encode the information of the state regardless of which way to encode it we choose? So instead of paying attention to just one of these possibilities, we use one abstract element? | |
| Aug 31, 2015 at 22:44 | history | answered | ACuriousMind♦ | CC BY-SA 3.0 |