Schrodinger Equation for a Bra Vector

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Discussion Overview

The discussion revolves around the derivation of the Schrödinger equation for a bra vector from its standard form, focusing on the treatment of complex conjugates and the implications of sign changes in the equation.

Discussion Character

  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant presents the Schrödinger equation for a bra vector and expresses confusion about the origin of the negative sign in the equation.
  • Another participant suggests that the bra function involves swapping the signs of complex numbers, which may clarify the sign issue when operating on the bra function.
  • A participant acknowledges a previous misunderstanding, noting the importance of conjugating all components, including the imaginary unit i, in the equation.
  • A later reply reiterates the need to conjugate everything and mentions that the imaginary unit can be moved to the numerator to address the negative sign when multiplied.

Areas of Agreement / Disagreement

Participants express individual understandings and corrections, but there is no consensus on the derivation process or the implications of the sign changes.

Contextual Notes

Participants do not fully resolve the derivation steps or the implications of the sign changes, leaving some assumptions and mathematical steps unaddressed.

nateHI
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The Schrödinger equation for the complex conjugate of a ket vector is:

d/dt<sai(t)| = -(<sai(t)|H)/(i*hcross)

How do you derive the above equation from the normal form of the Schrödinger equation? I'm mostly confused by where the negative sign is coming from.

Thanks
 
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The bra function has the signs of all complex numbers swapped, so by swapping the sign on the complex number in your equation when it operates on the bra function it gives the same result as if you operated on the ket without swapping the sign.
 
I get it now. I was making a silly mistake. You need to conjugate everything including the i in the denominator. Thanks.
 
nateHI said:
I get it now. I was making a silly mistake. You need to conjugate everything including the i in the denominator. Thanks.

You sometimes also see the i moved to the numerator since -(i/i) is the same as -1 but cancels out the negative sign when 2 of the i's are multiplied.
 

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