So would it be right to say that
A) Every quantum system is basicallly defined by a set of symmetries defined by a theorist. You pick them out.
B) These symmetries are defined as transformations that dont change the time-evolution equations, nature looks the same in different frames.
C)Mathematically this implies that if time evolution is defined by a Hamiltonian, assuming Schrodinger equation to be true, then any operator that commutes with the Hamiltonian is a symmetry and the hamiltonian is literally defined as the operator that commutes with all symmetries. Any operator that commutes with all given symmetries is a hamiltonian, thus defining additional symmetries "restricts" what a hamiltonian is. Not giving enough symmetries allows many options for a hamiltonian compatible with the required symmetries.
D) Not defining enough symmetries will make a theory very general and compatible with many results but then you can pick specific cases and say "case 1 is a posible Quantum system, case 2 is another quantum system" and so on, so its not so bad.
Tell me if this is a good interpretation of how quantum models are made.
E) Modeling a quantum system implies the tedious labor of building non-abstract mathematical objects you can do calculations on that represent the symmetries and the hamiltonian, which is just another operator that commutes with all the others BY DEFINITION but it must still be built.
Tell me if this is a good general approach.
A) Every quantum system is basicallly defined by a set of symmetries defined by a theorist. You pick them out.
B) These symmetries are defined as transformations that dont change the time-evolution equations, nature looks the same in different frames.
C)Mathematically this implies that if time evolution is defined by a Hamiltonian, assuming Schrodinger equation to be true, then any operator that commutes with the Hamiltonian is a symmetry and the hamiltonian is literally defined as the operator that commutes with all symmetries. Any operator that commutes with all given symmetries is a hamiltonian, thus defining additional symmetries "restricts" what a hamiltonian is. Not giving enough symmetries allows many options for a hamiltonian compatible with the required symmetries.
D) Not defining enough symmetries will make a theory very general and compatible with many results but then you can pick specific cases and say "case 1 is a posible Quantum system, case 2 is another quantum system" and so on, so its not so bad.
Tell me if this is a good interpretation of how quantum models are made.
E) Modeling a quantum system implies the tedious labor of building non-abstract mathematical objects you can do calculations on that represent the symmetries and the hamiltonian, which is just another operator that commutes with all the others BY DEFINITION but it must still be built.
Tell me if this is a good general approach.
