Formula- first order correction to the n-th wave func

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Discussion Overview

The discussion revolves around the expression of the first-order correction to the n-th wave function in quantum mechanics, specifically how it can be represented as a linear combination of other wave functions. Participants explore the theoretical underpinnings and implications of this representation, as well as inquiries into higher-order corrections.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asks for clarification on why the first-order correction to the n-th wave function can be expressed as a linear combination of other wave functions.
  • Another participant suggests that the wave functions form a basis for the vector space of wave functions, allowing for such linear combinations.
  • A different participant points out the need for clarification on the origin of the wave functions, referencing the Schrödinger equation to first order.
  • There is a curiosity expressed about how to expand the second-order correction to the wave function.
  • One participant notes that the referenced page for further reading does not load and mentions that higher-order corrections become increasingly complex.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and curiosity about the topic, with some seeking clarification while others provide insights. There is no consensus on the specifics of the wave functions or the corrections being discussed.

Contextual Notes

Some assumptions about the definitions and origins of the wave functions are not specified, which may affect the clarity of the discussion. The complexity of higher-order corrections is acknowledged but not elaborated upon.

Imperatore
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Could anybody explain me why indeed we can express the first-order correction to the n-th wave function [tex]\psi_{n}^{1}[/tex] by linear combination [tex]\sum_{m} c_{m}^{(n)}\psi_{m}^{o}[/tex]
 
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The ##\psi_n## (if defined properly - you didn't specify where they come from) are a base of your vector space of wave functions. You can express every physical wave function with such a linear combination.
 
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mfb said:
you didn't specify where they come from

It's Schrödinger equation to first order [tex]\lambda^{1}[/tex] You can see it on page 224 in the Griffiths' Introduction to quantum mechnics
 
So I am curious, how we can expand the 2-nd order correction to the wave function ? ;)

http://iate.oac.uncor.edu/~manuel/libros/Modern%20Physics/Quantum%20Mechanics/
 
That page doesn't load.

In a similar way, but the equations get progressively more messy with each order. I don't have the book here.
 

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