How is the transition amplitude formula derived from the Hamiltonian?

[Identity]

I'm reading through Peskin&Schroeder, and they mention that the probability of transition from a state $|\psi_0\rangle$ to a state $|\psi_1\rangle$ is given by:
$$\langle \psi_1|H|\psi_0\rangle$$
where $H$ is the Hamiltonian. Can someone please explain how this formula is derived? Thx

 

[Vanadium 50]

This is very basic QM.

I'm afraid that if this isn't immediately obvious to you, Peskin and Schroeder is too advanced for you. Have you taken undergrad QM? What book did you use?

 

[Identity]

Well, I've read most of Griffiths, but I think it may have been something I overlooked. Can you tell me? Thx

 

[Vanadium 50]

It's not something you overlook. This is one of the most basic aspects of quantum mechanics. I don't have Griffiths nearby, but Schiff devotes about 150 pages to this. If this isn't second nature to you, you aren't ready for Peskin & Schroeder. You'd be better served to go back to Griffiths and understand it before trying to move on.

 

[lugita15]

Maybe this is an equivalent formulation, but I've usually seen a unitary time evolution operator U which is an exponential of the Hamiltonian operator, not the Hamiltonian operator itself, being used in expressing the amplitude.

 

[Identity]

Maybe this is an equivalent formulation, but I've usually seen a unitary time evolution operator U which is an exponential of the Hamiltonian operator, not the Hamiltonian operator itself, being used in expressing the amplitude.

Yes, I've seen it in this form
$$|\psi\rangle = e^{-i\frac{H}{\hbar}t}|\psi(0)\rangle$$

I may look at Schiff to see if it is an equivalent formulation