Phase factor in quantum mechanics

In summary, the norm of a complex number can be calculated using the complex conjugate and is independent of the angle in the complex plane. This means that any complex number of the form ##e^{i\theta}## has a norm of 1. Also, any complex number can be written in the form ##re^{i\theta}##, where ##r## is the modulus and ##\theta## is the angle in the complex plane.
  • #1
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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  • #2
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. 🙂
 

1. What is the phase factor in quantum mechanics?

The phase factor in quantum mechanics is a mathematical concept that represents the complex phase of a wave function. It is a factor that multiplies the wave function and has no physical significance on its own, but it affects the overall behavior of the wave function.

2. How is the phase factor related to the probability of finding a particle in a certain state?

The phase factor does not directly affect the probability of finding a particle in a certain state. However, it can affect the interference patterns of the wave function, which in turn can affect the probability of finding a particle in a certain state.

3. Can the phase factor be measured or observed?

No, the phase factor is a mathematical concept and cannot be directly measured or observed. It is a theoretical tool used in quantum mechanics to describe the behavior of particles on a quantum level.

4. How does the phase factor change in different quantum systems?

The phase factor can change in different quantum systems depending on the properties of the system, such as the energy levels and interactions between particles. It is a dynamic factor that can change as the system evolves over time.

5. What are the physical implications of the phase factor in quantum mechanics?

The physical implications of the phase factor are seen in phenomena such as interference and superposition, which are fundamental aspects of quantum mechanics. It also plays a crucial role in quantum computing and other quantum technologies.

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