Why does the complex conjugate of psi pop out?

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Discussion Overview

The discussion centers on the concept of complex conjugates in relation to the modulus squared of a complex function, specifically in the context of quantum mechanics where the wave function, denoted as psi (Ψ), is involved. Participants explore the definition and properties of complex conjugates, as well as their application in calculating the modulus squared.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • One participant seeks to understand the definition of complex conjugates and their significance when calculating the modulus squared of psi.
  • Another participant defines the complex conjugate and outlines its properties, including how it is denoted and its geometric interpretation.
  • A third participant questions the phrasing of "pop out" in relation to the modulus squared of psi, seeking clarification on the term.
  • A later reply suggests that the expression Ψ*Ψ = |Ψ|² can be derived from the properties mentioned earlier, indicating a connection between the complex conjugate and the modulus squared.

Areas of Agreement / Disagreement

Participants generally agree on the definition and properties of complex conjugates, but the specific phrasing and implications of "pop out" remain unclear and are subject to further clarification.

Contextual Notes

The discussion does not resolve the underlying reasons for the terminology used or the implications of the relationship between complex conjugates and the modulus squared, leaving some assumptions and interpretations open-ended.

Indianspirit
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I just started teaching myself multivariable calculus and I know what the modulus of a complex number is but what is the complex conjugate and why does it pop out when we take the mod square of psi?

Like the first minute or two of video...

What are complex conjugates, how does one find them, etc...
 
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The conjugate of a complex number is what you get when you reverse the sign of the imaginary part of the number.
That is, the complex conjugate of ##a+bi## is ##a-bi##.
It is usually denoted by an asterisk, as in ##(a+bi)^*=a-bi##.
Complex conjugates have some neat properties, including that ##(z1+z2)^*=z1^*+z2^*;\ (z1\ z2)^*=z1^*\ z2^*##.
Also, ##z+z^*## is real and equal to double the real part of ##z##.
Geometrically in the Argand diagram, the complex conjugate of a number is its reflection in the real axis.
 
Indianspirit said:
why does it pop out when we take the mod square of psi?
What do you mean by "pop out"?
 
I think he means this: \Psi^* \Psi = |\Psi|^2
which can be deduced easily from the properties in andrewkirk's post.
 
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