Amplitude vs Magnitude: Explaining the Probability Density

[ParticleMan]

While trying to get a better understanding of amplitude vs magnitude, something I should frankly already know, the following video popped up near the top of my google search. Hmm...anything to point out? How many things?



But seriously, how would YOU explain amplitude vs magnitude? Would I be correct to say that the modulus squared of probability amplitude is a magnitude, the probability density?

 

[PeroK]

While trying to get a better understanding of amplitude vs magnitude, something I should frankly already know, the following video popped up near the top of my google search. Hmm...anything to point out? How many things?



But seriously, how would YOU explain amplitude vs magnitude? Would I be correct to say that the modulus squared of probability amplitude is a magnitude, the probability density?

You may be watching a video about telecommunications, not quantum mechanics!

 

[ParticleMan]

Actually it appears to be about Anatomy and Physiology, specifically dendrite communication. References are made to electricity. Regardless, I would expect the terminology for amplitude and magnitude to be the same.

So, Amplitude = electrical Amps. Amps are both power and frequency. Hmm...

Anyway...with a smile and a wink...back to my questions above?

 

[davenn]

So, Amplitude = electrical Amps. Amps are both power and frequency. Hmm...

no, that isn't correct

Amperes are Amperes and have nothing to do with amplitude or frequency

Amps relates to power (Watts) in that Amps x Volts = Watts (power)I'm trying to find a better description

 

[ParticleMan]

no, that isn't correct

LOL. I know. That’s what the tutor was teaching, sadly. Amps = Amperes which measure electrical current. I was just sharing the video, as I found it almost funny. Wondered if I ought to ask them to redo the video since it comes up so high in a google search.

I'm trying to find a better description

Just for for the difference between amplitude and magnitude, please. I think my statement above was correct with respect to probability amplitude vs probability density, but I’m not positive due to some other things I’ve read.

 

[PeroK]

Just for for the difference between amplitude and magnitude, please. I think my statement above was correct with respect to probability amplitude vs probability density, but I’m not positive due to some other things I’ve read.

A probability amplitude is a complex number, which has a magnitude and a polar angle $z = re^{i\theta}$.

In QM, the probability is the square of the magnitude of the probability amplitude, $r^2$ (in the discrete case) or the probability density in the continuous case.

 

[ParticleMan]

A probability amplitude is a complex number, which has a magnitude and a polar angle $z = re^{i\theta}$.

In QM, the probability is the square of the magnitude of the probability amplitude, $r^2$ (in the discrete case) or the probability density in the continuous case.

Thanks. Just trying to straighten out my terminology. From electronics, I think of the amplitude of waves being either positive or negative and based around zero, whereas the magnitude is only positive. Sounds like this is the same or at least similar.

 

[sophiecentaur]

@ParticleMan. When you find something that's not clear in an amateurish 'technical' Video on the Internet, the best thing to do is to do a search on the main terms that the video refers to and just read stuff. That way you will immerse yourself in the topic and, at the same time, find the way terms are used. Amplitude and Magnitude both refer to the Bigness of something. Amplitude is normally used to describe the maximum displace of an oscillation from the mean position (or perhaps zero). Magnitude is often used to describe the 'size' of a vector quantity. Magnitude and Direction are used to describe simple vectors.
There are instances where the word Magnitude is used in different contexts: The Magnitude of a Star refers to its brightness. "An order of Magnitude" can be used to imply that one value is ten times (or sometimes more) than another value.

It's largely just usage so don't let it bother you too much. PF can leave you more confused than before because the answers typically tend to follow a divergent path. Great fun for the contributors and often a good source of information but sometimes . . . . .

 

[ParticleMan]

@ParticleMan. When you find something that's not clear in an amateurish 'technical' Video on the Internet, the best thing to do is to do a search on the main terms that the video refers to and just read stuff. That way you will immerse yourself in the topic and, at the same time, find the way terms are used. Amplitude and Magnitude both refer to the Bigness of something.

Oh, definitely. Again, the video was high on the google search, and I thought it might be entertaining along with my question as well as being a representation of the kind of stuff that comes up in searches. This forum seems like a good place to ask questions of folks who seem to know. [Moderator's note: off topic comment deleted.] Making explanations more complicated than they need to be and then not adjusting as needed tends to stifle questions for some of us dummies for whom The Dummies series of books were written. LOL.

Amplitude is normally used to describe the maximum displace of an oscillation from the mean position (or perhaps zero). Magnitude is often used to describe the 'size' of a vector quantity. Magnitude and Direction are used to describe simple vectors.
There are instances where the word Magnitude is used in different contexts: The Magnitude of a Star refers to its brightness. "An order of Magnitude" can be used to imply that one value is ten times (or sometimes more) than another value.

Thank you. This is excellent and matches with what I thought. I was getting wrapped around the axle trying to relate this to probability amplitude. But I think I was getting mixed up thinking that the modulus of Psi squared was the probability amplitude, but I think it is actually the magnitude of the probability, as it was put earlier.

I went through computer engineering but became a glorified programmer, so I’ve unfortunately gotten pretty rusty over the years and have decided to brush up by re-learning what I’ve forgotten while developing a fascinating hobby.

It's largely just usage so don't let it bother you too much. PF can leave you more confused than before because the answers typically tend to follow a divergent path. Great fun for the contributors and often a good source of information but sometimes . . . . .

I’ve learned that precise definitions are pretty important for self learning, otherwise one can spend a long time struggling with something due to incorrect thinking. But I do think I understand what you mean. Thanks!

 

[sophiecentaur]

the video was high on the google search,

A high google ranking is not a good assessment of technical quality. Quite the reverse, sometimes.

ometimes it is difficult to tell the difference between those who just want to show off knowledge and make others feel inferior vs those who truly want to help others learn

PF is usually pretty good in that respect except that we can all get a tad too picky at times. Some PF members forget just how limited the knowledge of some questioners can be and leap into 'the hard stuff' whilst pointing out the ignorance of the OP's question. But you can usually rely on getting accurate information. If it isn't, then some other member will usually jump in a start a 'further discussion'
I always suggest a good textbook is a reliable source of correct terms but not everyone has one. The Hyperphysics site is excellent for concise bits of bookwork and equations and the terms they use are pretty reliable. It's hardly bed time reading though. The many videos by Walter Lewin are entertaining and full of good stuff. He tends to use the right words!

 

[ParticleMan]

The Hyperphysics site is excellent for concise bits of bookwork and equations and the terms they use are pretty reliable. It's hardly bed time reading though. The many videos by Walter Lewin are entertaining and full of good stuff. He tends to use the right words!

Funny you say that. I’m a bit of a strange bird, I guess. Night before last I was listening to Leonard Susskind before bed, and last night I was reading Dirac’ Quantum Mechanics. I try to flood myself with material from different perspectives because when one explanation doesn’t click, another one usually will. I’ll look into your Lewin recommendation. Any recommended Quantum Mechanics books for an autodidact? I’ve read a lot about Griffiths...

 

[Tom.G]

Now that was a deceiving video presentation! He was talking about neurological signalling in which he got the Frequency and Amplitude appropriate for that context, as far as he went. That description of Amps was really confusing but could be construed as correct... in that if you get an electrical shock the Neuron firing rate will increase with increased stimulation of the current.

Cheers,
Tom

 

[sophiecentaur]

Any recommended Quantum Mechanics books for an autodidact?

It depends entirely on the level you want to know about. How is your Maths? That will greatly affect what's best for you.

 

[ParticleMan]

It depends entirely on the level you want to know about. How is your Maths? That will greatly affect what's best for you.

If you're asking what I'm capable of, then the sky's the limit. Heh. If you're asking what I recall of Cal III and Differential Equations from my Engineering degree, not much these many years out from school I'm afraid.

Although I like material that spells things out in detail without skipping many steps, I'm not afraid of higher level material with the understanding that I will need to brush up as I go.

 

[jtbell]

From electronics, I think of the amplitude of waves being either positive or negative and based around zero, whereas the magnitude is only positive.

To me, as a physicist, the amplitude of a wave is the absolute value of the maximum displacement of the wave from zero in either direction (or rather from the centerline which may or may not be zero), and is therefore always positive. I've never used the term "magnitude" with respect to a wave. Maybe electrical engineers have a different convention.

[added] Now that I've fully read the other posts, I'd better say that my comments above are in the context of wave motion in classical mechanics, electronics, etc.

In quantum mechanics, "amplitude" also has the meaning of "probability amplitude" as described in one of PeroK's posts above. This is different from the "amplitude" that we use to describe a wave. In this context, "magnitude" is often used as a synonym for the modulus of a complex number.

In general, a QM probability is the square of the magnitude (modulus) of a (complex) probability amplitude.

Even in physics, which tends to use words more precisely than in common language, the same word can have different meanings in different contexts.

 

[davenn]

I think of the amplitude of waves being either positive or negative and based around zero, whereas the magnitude is only positive. Sounds like this is the same or at least similar.

No, I cannot go with that one

To me, as a physicist, the amplitude of a wave is the absolute value of the maximum displacement of the wave from zero in either direction (or rather from the centerline which may or may not be zero), and is therefore always positive. I've never used the term "magnitude" with respect to a wave. Maybe electrical engineers have a different convention.

agreedOK but here's an Amplitude and Magnitude difference that I should have thought of earlier

when using the Richter, ML or MB ( Local Magnitude Body wave Magnitude)
The Magnitude calculated for an earthquake is determined by using the maximum Amplitude of the waves on the seismogram

and those two cannot be reversed without the sentence sounding wrongD

 

[ParticleMan]

In quantum mechanics, "amplitude" also has the meaning of "probability amplitude" as described in one of PeroK's posts above. This is different from the "amplitude" that we use to describe a wave.

Ok. What makes probability amplitude different from amplitude with respect to a wave? Is it sort of an amplitude, or is the term truly an overloaded term?

Even in physics, which tends to use words more precisely than in common language, the same word can have different meanings in different contexts.

Good to be as precise as possible. I like to think that a lot of the complexity in physics and math has to do with overloaded and inconsistent terminology which makes learning difficult and irritates those who are incessantly questioned about the same terms.

 

[PeroK]

I like to think that a lot of the complexity in physics and math has to do with overloaded and inconsistent terminology which makes learning difficult and irritates those who are incessantly questioned about the same terms.

Most textbooks, in my experience, are precise and consistent about their terminology.

Although you may have developed your impression through watching too many YouTube videos.

 

[Vanadium 50]

I like to think that a lot of the complexity in physics and math has to do with overloaded and inconsistent terminology which makes learning difficult

I think starting in the middle is what causes this.

 

[ParticleMan]

[Moderator's note: off topic comment deleted.]

My theory of teaching has always been to have patience and provide answers kindly, even if for the umpteenth time, and to never discourage someone in their quest for knowledge. If someone does not understand something, it can be just as much the teacher’s fault for not probing well enough to understand the source of confusion and help solve it.

I started in a similar way, “in the middle”, with graduate and doctoral books, both 19th century and modern, when I began learning Greek and studying ancient manuscripts as a hobby. Now I can hold my own and can read Greek manuscripts in early uncial script as well as medieval manuscripts with their difficult minuscule ligatures.

Folks have different learning methods. I take something difficult, break it into constituent parts, study them, and put the parts back together until I’ve got it. A college-like structural approach is likely more efficient, but structure is not necessaily as easy for an autodidact, and since it is a hobby, it works for me.

 

[PeterDonis]

Some off topic posts (and part of one post) have been deleted. Please keep posts focused on the thread topic and do not veer off into personal comments.

 

[PeterDonis]

I like to think that a lot of the complexity in physics and math has to do with overloaded and inconsistent terminology

Different areas of science and math use different terminology for a reason. It looks like you are dipping into a lot of different areas at once, so yes, you are going to see the same terms used to mean very different things. But that's because you chose to look at a very broad range of topics at once, not because the people working in each of those fields are deliberately trying to confuse you. If you want to learn a lot of different fields, you have to accept what comes along with it. (Starting in the middle of a topic instead of at the most basic level can contribute to this too; people who write intermediate and advanced textbooks and papers in a field are building on the more basic work and writing for an audience who already knows it; they can't be expected to break everything down to a basic level the way an introductory text does.)

 

[ParticleMan]

Different areas of science and math use different terminology for a reason. It looks like you are dipping into a lot of different areas at once, so yes, you are going to see the same terms used to mean very different things. But that's because you chose to look at a very broad range of topics at once, not because the people working in each of those fields are deliberately trying to confuse you. If you want to learn a lot of different fields, you have to accept what comes along with it.(Starting in the middle of a topic instead of at the most basic level can contribute to this too; people who write intermediate and advanced textbooks and papers in a field are building on the more basic work and writing for an audience who already knows it; they can't be expected to break everything down to a basic level the way an introductory text does.)

First, my apology for the comment you deleted. I should have ignored the type of comments that frustrate me and focused on those that helped.

There are only 3 or 4 fields which I seriously study, but the terms should not overlap that much. The video I posted was not the main point, nor did I mean for anyone to infer that I thought it was intended to deceive anyone. I regret posting it and do not intend to discuss it further.

I don’t mean any disrespect, but I just don’t find it helpful to be told repeatedly that I am jumping into the “middle” of a subject and need to learn “the basics”. I know that. That’s why I am asking questions here and reading suggested literature.

 

[PeterDonis]

I just don’t find it helpful to be told repeatedly that I am jumping into the “middle” of a subject and need to learn “the basics”. I know that. That’s why I am asking questions here and reading suggested literature.

I'm not sure how asking about amplitude vs. magnitude will help you learn the basics (basics of what field?). Perhaps with some more context of how you came across these two terms and why you care about the difference between them would help.

 

[ParticleMan]

I'm not sure how asking about amplitude vs. magnitude will help you learn the basics (basics of what field?). Perhaps with some more context of how you came across these two terms and why you care about the difference between them would help.

No problem. As I mentioned earlier, I think, I was getting wrapped around the axle with respect to what QM probability amplitude meant, and it started making me question some basic assumptions about amplitude and magnitude. Sometimes one learns they’ve held incorrect notions for a long time. C’est ca.

 

[sophiecentaur]

I'm not sure how asking about amplitude vs. magnitude will help you learn the basics (basics of what field?).

I sense that the OP is confused when hopping from one topic to another. We have all been there. However, once you start from basics and follow a course through, the way terms are used is usually Defined and thereafter Consistent.
On the same lines, PF quite often gets perplexed questions about the common symbols used for different variables in different circumstances. "x" can be used to represent a dozen different quantitie in different books and papers and sometimes "x" or "y" can be used for the same quantity (and that in itself is an example). Working through from chapter one will avoid that sort of confusion.

 

[PeterDonis]

I think, I was getting wrapped around the axle with respect to what QM probability amplitude meant, and it started making me question some basic assumptions about amplitude and magnitude.

Where did the term "magnitude" come into it? The term "amplitude" does have a specific meaning in QM, as you say. But I've never seen the term "magnitude" used in QM. So where does it come in?