Intro to Quantum Mechanics - Formalism normalisation

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SUMMARY

The discussion focuses on the normalization of the quantum state coefficient c1, specifically addressing the relationship c1 = i c0, which introduces the complex number i into the normalization process. Participants clarify that the normalization yields i/sqrt(2) due to the absolute value squared of the complex number. The exponential form e^(iπ/2) is also discussed, illustrating the connection between complex numbers and quantum mechanics. This highlights the necessity of understanding complex coefficients in quantum state normalization.

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  • Understanding of complex numbers in mathematics
  • Familiarity with quantum mechanics terminology
  • Knowledge of normalization in quantum states
  • Basic grasp of Euler's formula e^(ix) = cos(x) + i sin(x)
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  • Study the implications of complex coefficients in quantum mechanics
  • Learn about quantum state normalization techniques
  • Explore Euler's formula and its applications in physics
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Graham87
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I can't figure out how they get i/sqrt(2) for normalisation of c1. Why is it a complex number? If I normalise c1 I just get 1/sqrt(2) because i disappears in the absolute value squared.

Thanks

1.png
 
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It looks like you left out other information from the problem, but apparently, there was the relation ##c_1 = i c_0##. That's where the ##i## comes from. Note that you had to have this relationship to solve for ##c_0##
otherwise you'd have two unknowns but only one equation.
 
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vela said:
It looks like you left out other information from the problem, but apparently, there was the relation ##c_1 = i c_0##. That's where the ##i## comes from. Note that you had to have this relationship to solve for ##c_0##
otherwise you'd have two unknowns but only one equation.

There was this relation:

1.png


Aha, so the exponential is also interpreted as i then. Thanks, got it!
 
##e^{i\pi/2}= \cos (\pi/2) + i \sin(\pi/2) = i##
##e^{iv}= \cos (v) + i \sin(v) ##
 
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