1st order pertubation on 2 level system

This is due to the formula for the first-order correction to the wave function, which takes into account the difference in energy levels. You are not wrong, and your confusion is understandable.
  • #1
luxiaolei
75
0
Hi all. I m stucked on the question followed, any helps will be greatly appreciated.

A perturbation has the form H'=z act on a two level system which they have different parity.

So the first order correction to the energy level 1 and 2 are give by:

E11=<ψ1| H' |ψ1>

Same for level 2.

These two energy correction are clearly zero because the same level has same parity.

However the first order wavefunction corrections are not for both level:

According to time independent non-degenerate perturbation theory on the 1st order correction to the wave function formula:

ψ11=<ψ2| H ' | ψ1>/(E1-E2) ψ2

Which is none zero

Where am I wrong? I am so confused..thanks in advance.
 
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  • #2
Your understanding is correct. The first-order energy corrections for both levels are zero, since they have the same parity and H' has the form z. However, the first-order wavefunction corrections are not zero, as you have calculated correctly.
 

FAQ: 1st order pertubation on 2 level system

1. What is first order perturbation on a 2 level system?

First order perturbation on a 2 level system refers to the mathematical technique used to analyze the effects of a small perturbation or disturbance on the energy levels of a quantum system with only two possible states.

2. How is first order perturbation calculated?

To calculate first order perturbation on a 2 level system, one must first determine the unperturbed energy levels of the system. Then, the perturbation term is added to the Hamiltonian matrix and the new energy levels are calculated using the Schrödinger equation.

3. What is the importance of first order perturbation in quantum mechanics?

First order perturbation is important in quantum mechanics as it allows us to understand the effects of small perturbations on the energy levels of a system. This is crucial in predicting and analyzing the behavior of quantum systems in real-world applications.

4. Can first order perturbation be applied to systems with more than 2 levels?

Yes, first order perturbation can be applied to systems with more than 2 levels. However, the calculations become more complex as the number of energy levels increases.

5. What are some limitations of first order perturbation?

One limitation of first order perturbation is that it assumes the perturbation is small enough to only cause slight changes in the energy levels. It also does not take into account higher order perturbations, which may have a larger impact on the system.

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