Intro to Quantum Mechanics - Formalism normalisation

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The discussion centers on the normalization of the coefficient c1 in quantum mechanics, specifically why it is expressed as i/sqrt(2). The presence of the complex number i arises from the relationship c1 = i c0, which is necessary to solve for c0 given the constraints of the problem. Participants clarify that without this relationship, there would be two unknowns with only one equation, complicating the normalization process. The exponential function is also linked to the complex number, illustrating how e^(iπ/2) simplifies to i. Understanding these relationships is crucial for grasping the formalism of quantum mechanics.
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

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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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I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW

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