Phase factor in quantum mechanics

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Homework Help Overview

The discussion revolves around the properties of complex numbers in the context of quantum mechanics, specifically focusing on the phase factor represented by expressions of the form ##e^{i\theta}##.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the absolute value of complex numbers, questioning why numbers of the form ##e^{i\theta}## have a modulus of 1. There are requests for explanations regarding the calculation of norms and the relationship between a complex number and its conjugate.

Discussion Status

Several participants are actively seeking clarification on the properties of complex numbers, particularly regarding their norms. Some guidance has been provided on how to compute the norm using the complex conjugate, but the discussion remains open with multiple requests for further explanation.

Contextual Notes

Participants express a need for foundational understanding, indicating that some may find the concepts elementary while others are still grappling with them. There is an acknowledgment of varying levels of familiarity with the topic.

Shreya
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Homework Statement
I watched a lecture in which the professor called the circle expression as a pure phase and took its absolute value to be 1. I don't understand how it's absolute value is 1.
Please refer the image for the circled expression.
Relevant Equations
Wave function at x,t
Please be kind to help.I would be grateful
IMG_20211112_125534~2.jpg
 
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Any complex number of the form ##e^{i\theta}## has absolute value (modulus) ##1##.
 
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Can you please explain why is it so?
 
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Shreya said:
Can you please explain why is it so?
The norm of a complex number can be calculated using the number ##z## and ##z^*=\bar{z}## the complex conjugate.
So, given ##z=e^{i\theta}, \quad \theta \in \mathbb{R}##, you should be able to compute ##z^*## and its norm.
You will see that the norm is 1 independent on ##\theta##.
 
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Shreya said:
Can you please explain why is it so?
Any complex number can be written ##re^{i\theta}##, where ##r## is the modulus and ##\theta## is the angle in the complex plane. That's fairly elementary, I'm sorry to say!
 
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Thanks a lot 🙏 Pero K and Gaussian97! It helped a lot. 🙂
 

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