(adsbygoogle = window.adsbygoogle || []).push({}); Dirac's "Quantum Mechanics" - the definition of the time evolution operator

I'm reading Dirac's "Principles Of Quantum Mechanics" to learn more about the formal side of the subject.

I have a question about the way he defines the time evolution operator in the book. Either there's a mistake or I'm missing something.

In chapter 27 he says (eqn 1) that [itex]\hat{T}[/itex] is defined such that:

[itex]|P(t)> = \hat{T} |P(0)>[/itex]

Where |P(0)> is a ket at time t=0 , and |P(t)> - at time t

Or equivalently |P(0)> is a ket in the Heisenberg picture, and |P(t)> - in the Schrodinger picture.

So this implies that:

[itex]<P(t)| = <P(0)| \hat{T}^{\dagger} [/itex]

And then in chapter 32, eqn 45 implies that:

[itex]<P(t)| = <P(0)| \hat{T} [/itex]

And I understand, that we can define it both ways, since it's a unitary operator. But we should stick to one way of defining it, and I'm sure Dirac does. So what it is here, that I'm not understanding properly?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Dirac's Quantum Mechanics - the definition of the time evolution operator

**Physics Forums | Science Articles, Homework Help, Discussion**