1st order Pertubation energy and wavefunction

In summary, the conversation discusses the first order correction of the perturbed energy, which is calculated for a specific eigenvector of the Hamiltonian. It cannot be a superposition of multiple eigenvectors. The question also asks if the unperturbed solution, ψn0, can be a general solution or has to be a specified state vector, to which the answer is that it has to be a specified state vector.
  • #1
luxiaolei
75
0
Hi all,

I must misunderstood somewhere, couldn't figure out the following, any helps will be greatly appreciated.

The first order correction of the pertubated energy is:

[itex]\leftψn0\langle[/itex] H'[itex]\rightψn0\rangle[/itex]

Where:
ψn0
Is the solution of the unpertubated Hamiltonian.

My question is can ψn0 be the general solution to the Hamiltonian or has to be a specified state vector?

i.e.,

ψn0= aψ10+bψ20

Or has to be:

ψn0=ψ10

If it can be the superposition of the eigenstates, then how to construct the first order wave function?
Thanks in advance:)
 
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  • #2
The correction is calculated for a particular eigenvector of the Hamiltonian and not for a superposition of several eigenvectors.
 
  • #3
dextercioby said:
The correction is calculated for a particular eigenvector of the Hamiltonian and not for a superposition of several eigenvectors.

Thank you so much!
 

FAQ: 1st order Pertubation energy and wavefunction

1. What is 1st order perturbation energy and wavefunction?

1st order perturbation energy and wavefunction is a concept in quantum mechanics that describes the changes in the energy and wavefunction of a quantum system due to a small external perturbation. It takes into account the effects of the perturbation on the original system and calculates the resulting energy and wavefunction.

2. How is 1st order perturbation energy and wavefunction calculated?

The 1st order perturbation energy and wavefunction can be calculated using the first-order perturbation theory. This involves finding the expectation values of the perturbation Hamiltonian and the unperturbed Hamiltonian, and then using these values to solve for the changes in energy and wavefunction.

3. What is the importance of 1st order perturbation energy and wavefunction in quantum mechanics?

1st order perturbation energy and wavefunction is important because it allows us to understand the behavior of quantum systems under the influence of external perturbations. This is crucial in areas such as quantum chemistry and material science, where small changes in the system can have significant effects.

4. Can 1st order perturbation energy and wavefunction be applied to any quantum system?

Yes, the first-order perturbation theory can be applied to any quantum system, as long as the perturbation is small enough to be treated as a small deviation from the original system. However, for larger perturbations, higher-order perturbation theories may be needed.

5. How does 1st order perturbation energy and wavefunction differ from 2nd or higher order perturbation theories?

1st order perturbation energy and wavefunction only takes into account the effects of the first-order changes in the perturbation, while higher-order perturbation theories consider higher-order changes. This means that 1st order perturbation is an approximation and may not accurately describe the system for larger perturbations.

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