Intro to Quantum Mechanics - Formalism normalisation

AI Thread Summary
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
Messages
72
Reaction score
16
Homework Statement
See pic
Relevant Equations
See pic
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
 
Physics news on Phys.org
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.
 
  • Like
Likes topsquark and Graham87
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) ##
 
  • Like
Likes SammyS, topsquark and Graham87
Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'
(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.) I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of...

Similar threads

Back
Top