I have a puzzle about Schroedinger equation with time-dependent hamiltonian, which is usually used in time-dependent quantum systems.

However, one of the axioms in quantum mechanics postulates that the hamiltonian as the generator of the one-parameter unitary group $U(t)$ is not time-dependent, and the evolution of a quantum state should obey the Schroedinger equation with time-independent hamiltonian.

So why can Schroedinger equation with time-dependent hamiltonian be used without hesitation?

Where does the time-dependent hamiltonian come from, except for the case of interaction picture? And should there be an additional axiom for it?

I have a puzzle about Schroedinger equation with time-dependent hamiltonian, which is usually used in time-dependent quantum systems.

However, one of the axioms in quantum mechanics postulates that the hamiltonian as the generator of the one-parameter unitary group $U(t)$ is not time-dependent, and the evolution of a quantum state should obey the Schroedinger equation with time-independent hamiltonian.

So why can Schroedinger equation with time-dependent hamiltonian be used without hesitation?

Where does the time-dependent hamiltonian come from, except for the case of interaction picture? And should there be an additional axiom for it?

The key is to recognize which are from axiom and which are from model. I foolishly thought that every Shroedinger equation with a time-dependent Hamiltonian can be derived by starting from that strong-continuity axiom in quantum mechanics. Also, I do not think the above comments answered my question.

I have a puzzle about Schroedinger equation with time-dependent hamiltonian, which is usually used in time-dependent quantum systems.

However, one of the axioms in quantum mechanics postulates that the hamiltonian as the generator of the one-parameter unitary group U(t) is not time-dependent, and the evolution of a quantum state should obey the Schroedinger equation with time-independent hamiltonian.

So why can Schroedinger equation with time-dependent hamiltonian be used without hesitation?

Where does the time-dependent hamiltonian come from, except for the case of interaction picture? And should there be an additional axiom for it?

I have a puzzle about Schroedinger equation with time-dependent hamiltonian, which is usually used in time-dependent quantum systems.

However, one of the axioms in quantum mechanics postulates that the hamiltonian as the generator of the one-parameter unitary group $U(t)$ is not time-dependent, and the evolution of a quantum state should obey the Schroedinger equation with time-independent hamiltonian.

So why can Schroedinger equation with time-dependent hamiltonian be used without hesitation?

Where does the time-dependent hamiltonian come from, except for the case of interaction picture? And should there be an additional axiom for it?