- #1
diegzumillo
- 173
- 18
Presentation - "A study on the Dyson series"
Hi there,
I'm not sure this is the right place to talk about this. If not, please indicate me where I can take this. :]
I wrote a dissertation about the Dyson series, as a requirement for my bachelor degree. It's not very long, but for the presentation I have to filter something! I'm listing here the topics covered, and if anyone has any suggestions on what to talk about, I'll sure apreciate it! :]
-Introduction: Nothing really substantial here. Just a really brief history of the series, motivations for quantum mechanics, etc.
-Quantum mechanics fundamentals: Hilbert space, Dirac notation and postulates.
-Time evolution operator and the Dyson series: Definition and properties like unitarity and convergence.
-Schrödinger, Heisenberg and interaction picture.
-Transition probability: The point here is how to obtain approximate results using the Dyson series. Furthermore, there is a physical interpretation and specification to Hamiltonian eigenstates.
-Constant perturbation (or step perturbation): We calculate the transition amplitude for a system with a constant perturbation (turned on after t=0).
-Harmonic oscilattor with a harmonic perturbation: We calculate the transition amplitude. The difference is that the calculations are really, really extensive!
For now, I'm preparing the presentation skipping the fundamentals: Evolution operator, transition amplitude and the applications.
So... What would you like to hear? If you were forced to sit down and listen to this for 50 minutes, or something.
Hi there,
I'm not sure this is the right place to talk about this. If not, please indicate me where I can take this. :]
I wrote a dissertation about the Dyson series, as a requirement for my bachelor degree. It's not very long, but for the presentation I have to filter something! I'm listing here the topics covered, and if anyone has any suggestions on what to talk about, I'll sure apreciate it! :]
-Introduction: Nothing really substantial here. Just a really brief history of the series, motivations for quantum mechanics, etc.
-Quantum mechanics fundamentals: Hilbert space, Dirac notation and postulates.
-Time evolution operator and the Dyson series: Definition and properties like unitarity and convergence.
-Schrödinger, Heisenberg and interaction picture.
-Transition probability: The point here is how to obtain approximate results using the Dyson series. Furthermore, there is a physical interpretation and specification to Hamiltonian eigenstates.
-Constant perturbation (or step perturbation): We calculate the transition amplitude for a system with a constant perturbation (turned on after t=0).
-Harmonic oscilattor with a harmonic perturbation: We calculate the transition amplitude. The difference is that the calculations are really, really extensive!
For now, I'm preparing the presentation skipping the fundamentals: Evolution operator, transition amplitude and the applications.
So... What would you like to hear? If you were forced to sit down and listen to this for 50 minutes, or something.