Writing perturbed wave function

In summary, the conversation discusses the construction of a wave function for a perturbed system. The original wave function has solutions for even and odd n-values, while the perturbed wave function also has even and odd solutions. The question is whether the value of k in the attachment needs to follow the same even/odd pattern as the n-values. TheBlueDot is reminded to use the PF LaTeX feature for posting equations.
  • #1
TheBlueDot
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Hello,

I'm trying to write a wave function for a perturbed system. The original (unperturbed) wave function has two solutions for even and odd n-values, for example ##sin(n \pi x)## for even-n and ##cos(n\pi x)## for odd-n. Then, the perturbed wave function also has an even and odd solutions. My question is does ##k^{(0)}## in the attachment also need to be even or odd according to even and odd n-values?Thanks!
 

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FAQ: Writing perturbed wave function

1. What is a perturbed wave function?

A perturbed wave function is a mathematical representation of the state of a quantum system that has been disturbed or altered by an external force or potential. It describes the probability of finding a particle in a specific location or state after being subjected to a perturbation.

2. How is a perturbed wave function calculated?

The perturbed wave function is calculated using the Schrödinger equation, which is a fundamental equation in quantum mechanics that describes how a system evolves over time. The equation takes into account the perturbing potential and the original wave function of the system to determine the new perturbed wave function.

3. What is the significance of the perturbed wave function in quantum mechanics?

The perturbed wave function is an important concept in quantum mechanics as it allows us to understand and predict the behavior of quantum systems when subjected to external forces. It helps us to study the effects of perturbations on the states and properties of particles, which is essential in fields such as atomic and molecular physics, solid-state physics, and quantum chemistry.

4. Can the perturbed wave function be experimentally observed?

No, the perturbed wave function cannot be directly observed experimentally. It is a mathematical representation of the state of a quantum system and cannot be measured directly. However, its effects on the behavior of particles can be observed and measured through experiments.

5. Are there any limitations to using perturbed wave functions?

There are some limitations to using perturbed wave functions, as they assume that the perturbation is small and that the system is in a stable state. In reality, many systems are subject to large perturbations and may not be in a stable state. In these cases, more advanced mathematical techniques, such as perturbation theory, may be necessary to accurately describe the system.

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