First order perturbation theory problem

In summary, first order perturbation theory is a mathematical technique used in quantum mechanics to approximate the energy levels and wavefunctions of a system when a small perturbation is applied. It is applicable when the perturbation is small and turned on for a short period of time, and is based on assumptions such as the perturbation being small and the unperturbed eigenstates forming a complete set. In practice, it is used to calculate energy corrections and wavefunctions by solving the perturbed Schrödinger equation. However, limitations include the need for small perturbations and short application times, and it may not account for interactions between multiple perturbations. Higher order perturbation theory may be needed for more accurate results in these cases.
  • #1
Bowenwww
25
0
Ok so I have a classic particle in a box problem. If a particle in a box, the states of which are given by: ψ = (√2/L) * sin(nπx/L) where n=1,2,3...

is perturbed by a potential v(x) = γx , how do I calculate the energy shift of the ground state in first order perturbation

I'm guessing that the energy shift is given by the expectation value of this perturbation but apart from that I'm stumped.

Thanks in advance guys
 
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  • #2
hint: you should calculate the expectation of the perturbation with respect to which state?
 

FAQ: First order perturbation theory problem

What is first order perturbation theory?

First order perturbation theory is a mathematical technique used in quantum mechanics to approximate the energy levels and wavefunctions of a system when a small perturbation is applied to the system's Hamiltonian. It allows for the calculation of more accurate results compared to the unperturbed system.

When is first order perturbation theory applicable?

First order perturbation theory is applicable when the perturbation is small compared to the energy differences between the unperturbed states of the system. It is also valid when the perturbation is turned on for a short period of time.

What are the assumptions made in first order perturbation theory?

The assumptions made in first order perturbation theory include: the perturbation is small, the unperturbed eigenstates form a complete set, and the perturbed and unperturbed Hamiltonians have the same eigenvectors.

How is first order perturbation theory used in practice?

In practice, first order perturbation theory is used to calculate the energy corrections and wavefunctions of a system by solving the perturbed Schrödinger equation. These results can then be compared to experimental data to verify the accuracy of the theory.

What are the limitations of first order perturbation theory?

First order perturbation theory has limitations when the perturbation is not small or when the perturbation is applied for a long period of time. It also does not take into account interactions between multiple perturbations, and higher order perturbation theory may be needed for more accurate results in these cases.

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