What exactly is meant by a phase in Quantum Mechanics?

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SUMMARY

The discussion clarifies the concept of "phase" in Quantum Mechanics, defining it as a representation of a specific position within a periodic cycle, akin to angles in oscillations. Participants explain that phase can be quantified using degrees or radians, with examples drawn from wave behavior and periodic phenomena like moon phases. The Fourier transform is highlighted as a method for determining phase relationships theoretically, while interferometers serve as experimental tools. Overall, understanding phase is essential for grasping wave behavior in quantum physics.

PREREQUISITES
  • Basic understanding of Quantum Mechanics principles
  • Familiarity with wave behavior and oscillations
  • Knowledge of Fourier transforms
  • Experience with interferometry techniques
NEXT STEPS
  • Study the Fourier transform in detail and its applications in Quantum Mechanics
  • Explore the principles of interferometry and its role in measuring phase
  • Learn about wave-particle duality and its implications in Quantum Mechanics
  • Investigate the mathematical representation of oscillations and their phases
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Students and professionals in physics, particularly those focused on Quantum Mechanics, wave behavior, and experimental methodologies in physics.

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I understand this is probably a very stupid question to some of the people on here, but none the less i would still like to know. It hasn't been explained very well to me.
I have a vague understanding that it is a number that you collect for each possible path? Please correct/elaborate on this if possible?
I was also told the phase represents the position in the cycle of a wave, whether it is at a crest or trough or some precise position in between. How do find the position it represents and how can you label an infinite number of paths with phases? How do you find the position in the cycle of a wave?
 
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Phase relationships are determined theoretically by taking the Fourier transform of the fields or waves, and experimentally using interferometers.

This might be interesting:

Book review: Neutron Interferometry: Lessons in Experimental Quantum Mechanics
http://www.trincoll.edu/~silverma/reviews_commentary/neutron_interferometry.html
 
A phase of anything is one part of a periodic behavior. Take the moon phases as an example, it goes full - half - crescent - half - full , etc in a periodic manner, and a particular part of that cycle, say for example the full moon is a phase of the whole cycle. And roughly a month later the same phase happens again. The same is true for any periodic behavior, including waves, that go between crests and troughs. We then characterize a full cycle as a number, like 360 degrees or 2*pi radians, which gives us more accuracy in determining where in the cycle we are. The starting point is arbitrary, and we could for example choose a crest in a wave to correspond to 0 degrees, and from that it would follow that the trough would be at 180 degrees.

Waves are often encoutered in physics, especially in quantum physics, coming from the wave nature of objects, and when we talk about a phase angle here, we talk about exactly the same thing as I mentioned above: a particular part of a periodic behavior compared to a chosen starting/reference point.

I hope that somewhat simple/fundamental explanation helped.
 
Thank you all for your Input ! I appreciate it.
 

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