Breakdown of perturbation expansion

This ratio will eventually grow larger than the size of the perturbation, causing the perturbation expansion to break down. This is due to the fact that the perturbation grows faster than the unperturbed energy as n increases.
  • #1
commutator
13
0

Homework Statement

consider a perturbation to the simple harmonic oscillator problem Lambda* (x)^4
question a) show tht the first order correction to n-th eigenstate is proportional to (1+2n+2n^2)
b) argue that no matter how small lambda is ,the perturbation expansion will break down for some large enough "n."
what is the physical reason?


Homework Equations

relations are scrodinger equation and raising and lowering operators.



The Attempt at a Solution

a)i have worked out.
but i do not know how to proceed for part b.
any help will be highly appreciated. many thanks in advance.:P
 
Physics news on Phys.org
  • #2
You might want to compute the ratio of the correction to the unperturbed energy.
 

1. What is the concept of perturbation expansion?

Perturbation expansion is a mathematical method used to approximate the solutions of a complex problem by breaking it down into simpler, solvable parts. It is based on the assumption that the problem can be solved by adding small corrections to a known solution.

2. How does perturbation expansion work?

Perturbation expansion involves breaking down a complex problem into a simpler form, which can be solved using known mathematical techniques. The solution obtained from this simplified problem is then used to approximate the solution of the original problem by adding small corrections.

3. What are the limitations of perturbation expansion?

One limitation of perturbation expansion is that it only works for problems where small corrections can be added to a known solution. It is not suitable for problems with large uncertainties or nonlinearities. Additionally, the accuracy of the approximation decreases as the order of perturbation increases.

4. What are the applications of perturbation expansion in science?

Perturbation expansion is widely used in various fields of science, including physics, chemistry, and engineering. It is particularly useful in analyzing systems with small deviations from a known solution, such as the motion of celestial bodies, the behavior of atoms, and the stability of structures.

5. How is perturbation expansion different from other approximation methods?

Unlike other approximation methods that aim to solve the problem directly, perturbation expansion breaks it down into simpler parts and uses known solutions to approximate the solution of the original problem. It is also more suitable for problems with small perturbations, whereas other methods may be more accurate for larger perturbations.

Similar threads

QFT for Gifted Amateur - Problem 2.2
    • Advanced Physics Homework Help
Replies
1
Views
1K
I About time-independent non-degenerate perturbation expansion
    • Quantum Physics
Replies
3
Views
723
I More doubts in perturbation theory
    • Quantum Physics
Replies
8
Views
850
How do you plot eigenfunctions of perturbed HO?
    • Advanced Physics Homework Help
Replies
9
Views
2K
First Order Perturbation Theory - QM
    • Advanced Physics Homework Help
Replies
1
Views
2K
Why are unperturbed states valid basis for perturbed system?
    • Advanced Physics Homework Help
Replies
4
Views
1K
Weinberg 3.4 -- Derive the perturbation expansion....
    • Advanced Physics Homework Help
Replies
5
Views
2K
Question on Time-Independent Perturbation Theory
    • Introductory Physics Homework Help
Replies
3
Views
599
How to explain the Quantum Mechanics/Math of the stages of MRI imaging
    • Advanced Physics Homework Help
Replies
4
Views
1K
A Does there exist a proof for these conjectures?
    • Quantum Physics
Replies
2
Views
986

Hot Threads

Recent Insights

Back
Top