Time-dependent perturbation theory question not a hard one

In summary, we have a hydrogen atom in a uniform electric field with a time-dependent function. We are asked to find the probability of the atom transitioning from its initial ground state to the 2p state as t approaches infinity. There is some confusion about which state the 2p state refers to, but it is ultimately determined to be the state with n=2 and l=1. This is because the electric dipole transition requires a change in l by 1.
  • #1
bojibridge
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0

Homework Statement



A hydrogen atom is placed in a uniform electric field E(t) given by E(t) = Enaught*exp(-a*t) (where a is a constant) for t >0.

The atom is initially in the ground state. What is the probability that, as
t→∞ , the atom makes a transition to the 2p state?

I know how to do this problem in general, but I'm just curious if by 2p state it means |2 0 0> or |2 1 0>...I want to go with the former, but is that what others would do? Or is it even going to matter?

Thanks so much!
 
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  • #2
2s would mean n=2, l=0; 2p means n=2, l=1. If I recall correctly, the electric dipole transition ends up requiring l to change by 1.
 
  • #3
Ah, yes, of course! Thank you! I'd lose my head if it wasn't attached...
 

1. What is time-dependent perturbation theory?

Time-dependent perturbation theory is a mathematical tool used in quantum mechanics to study the behavior of a quantum system when it is subject to an external force or perturbation that varies with time. It allows us to calculate the probability of a quantum system transitioning from one state to another over time.

2. How does time-dependent perturbation theory differ from time-independent perturbation theory?

While time-independent perturbation theory deals with systems that are subject to a constant external perturbation, time-dependent perturbation theory takes into account the time-varying nature of the perturbation. This allows us to study more complex systems and their behavior over time.

3. What are the applications of time-dependent perturbation theory?

Time-dependent perturbation theory has many applications in physics, chemistry, and other fields. It is used to study the behavior of atoms and molecules in electromagnetic fields, the interaction of light with matter, and the dynamics of chemical reactions, among others.

4. What are the main principles of time-dependent perturbation theory?

The main principles of time-dependent perturbation theory include the time-dependent Schrödinger equation, the time-evolution operator, and the perturbation expansion. These principles allow us to calculate the probability of a quantum system transitioning from one state to another over time.

5. How is time-dependent perturbation theory used in practical experiments?

Time-dependent perturbation theory is used in practical experiments by measuring the response of a system to a time-varying perturbation and then comparing it to the theoretical predictions. This allows us to verify the accuracy of the theory and make predictions about the behavior of similar systems in the future.

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