Schrodinger equation in terms of complex conjugate

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SUMMARY

The discussion focuses on the application of the complex conjugate in the Schrödinger equation (S.E) and the implications of conjugating the wave function ψ. It clarifies that the derivative with respect to time, when expressed in terms of the complex conjugate ψ*, remains valid as long as the original equation is valid. Key c-number conjugation rules are highlighted, including the conjugation of products and sums, as well as the derivative of the wave function. The importance of the product rule in this context is emphasized, aiding in the understanding of the equation's transformation.

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I know there's a similar post, but i didn't understand it. Why the derivative respect to t in terms of the complex conjugate of ψ is:
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instead of being the original S.E in terms of ψ*
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or the equation in terms of ψ with the signs swapped
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One is simply applying conjugation to the equation as a whole. This yields an equation which is valid provided the original is valid. Some c-number conjugation rules that may be helpful are,

  1. ##(a b)^\ast = a^\ast b^\ast##
  2. ##(a + b)^\ast = a^\ast + b^\ast##
  3. ##(i)^\ast = -i##
  4. ##(\frac{\partial \psi}{\partial t})^\ast = \frac{\partial \bar\psi}{\partial t}##
 
I got it!. I always forget to use the product rule, Thanks
 

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