Tough Perturbation Question (At least for me)

In summary, the conversation discusses the energies of a particle confined in a two dimensional square well and how they are affected by a perturbation. The experts advise identifying the basis, computing the perturbation matrix, and solving the system of equations using time-independent degenerate perturbation theory. A helpful resource for this topic is also provided.
  • #1
Ed Quanta
297
0
Consider a particle confined in a two dimensional square well with faces at x=0,a;y=0,a. The doubly degenerate eigenstates appear as Psinp=(2/a)sin(n(pi)x/a)sin(p(pi)x/a)
Enp=E1(n^2 + p^2)

What do these energies become under perturbation H'=10^-3E1sin((pi)x/a)?

Help anyone? No idea how to solve this.
 
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  • #2
There's not too much advice to give,just apply the theory strictly.Identify the basis,compute the pertubation matrix and then write the system of equations.

Daniel.
 
  • #3
I agree, this is about as plug-and-chug as it gets. Ed, have you read the relevant material in your textbook? This is a straightforward exercise in time-independent degenerate perturbation theory.

edit:

Here's a nice summary:
http://electron6.phys.utk.edu/qm2/modules/m8/degenerate.htm
 
Last edited:

Related to Tough Perturbation Question (At least for me)

1. What is a "Tough Perturbation Question"?

A "Tough Perturbation Question" is a type of scientific question that involves manipulating an existing system or process in order to understand how it responds to different conditions or stimuli. This can involve changing one or more variables and observing the resulting effects.

2. How do you design experiments to answer Tough Perturbation Questions?

To design experiments to answer Tough Perturbation Questions, scientists must carefully identify the variables that they want to manipulate or observe and determine the appropriate conditions or stimuli to use. They must also establish control groups and methods for measuring and analyzing the data collected.

3. What are the benefits of using Tough Perturbation Questions in scientific research?

Tough Perturbation Questions can provide valuable insights into how systems and processes function and respond to changes. They can also help identify key variables and mechanisms that contribute to specific outcomes, leading to a deeper understanding of complex phenomena.

4. What are some challenges associated with conducting experiments involving Tough Perturbation Questions?

One challenge is ensuring that the perturbations or changes implemented do not have unintended effects on the system being studied. Another challenge is designing experiments that accurately reflect real-world conditions and can be replicated by other scientists.

5. How can scientists effectively communicate and share findings from experiments involving Tough Perturbation Questions?

To effectively communicate findings from Tough Perturbation Questions, scientists must clearly explain the methods and procedures used, present the data and results in a comprehensive and transparent manner, and discuss the implications and limitations of their findings. They should also make their data and methods publicly available for other researchers to replicate and build upon.

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