- #1
Sammywu
- 273
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I just read a few articles introducing the basic concept of QM.
I found QM is built as a model of a statespace over a background of 3-dim space.
Observables are just Hermitian operators on this statespace.
Position is an Hermitian operator on this statespace as well. The classical position is basically the expectational value of this operator.
Momentum is a Hermitian operator as the generator of space translation.
If we just make the background as a timespace manifold, Hamiltonian can be the generator of time translation instead of time evolvement. Why do we need this time evolvement in place to make things more complicated?
Also, I found that the concept of two particles shall not occupy the same state in this statespace is natural. I don't see why only Fermions need to comply to this Pauli Exclusion Principle.
Regards
I found QM is built as a model of a statespace over a background of 3-dim space.
Observables are just Hermitian operators on this statespace.
Position is an Hermitian operator on this statespace as well. The classical position is basically the expectational value of this operator.
Momentum is a Hermitian operator as the generator of space translation.
If we just make the background as a timespace manifold, Hamiltonian can be the generator of time translation instead of time evolvement. Why do we need this time evolvement in place to make things more complicated?
Also, I found that the concept of two particles shall not occupy the same state in this statespace is natural. I don't see why only Fermions need to comply to this Pauli Exclusion Principle.
Regards