Help explaining a quantum wave function. (How you describe a wave by a particle)

[nukeman]

I understand a normal mechanical wave, simply a disturbance that moves.

But, I want understand a quantum wave function, mainly how you can describe a wave by the particle it self?

 

[Amok]

I understand a normal mechanical wave, simply a disturbance that moves.

But, I want understand a quantum wave function, mainly how you can describe a wave by the particle it self?

You can't. The meaning of the word 'particle' is not the same as in a classical context (something like a little marble). A wave-function is not a wave in the classical sense either; in fact Schroedinger's equation is not a wave equation. Some physical objects/systems seem to display both properties that we have come to associate with waves or particles (depending on the circumstances). Turns out they're neither (in the classical sense), they're quantum mechanical objects (or more generally quantum physical objects).

 

[mercrave]

So why do people call it the Schrödinger Wave Equation? Because it's derived from the electromagnetic wave equation? Or is because superposition between quantum mechanical objects act kind of like waves? (bear with me, I'm not sure I understand my own question, I'm just an undergrad and I've only taken a modern physics course)

 

[ZapperZ]

So why do people call it the Schrödinger Wave Equation? Because it's derived from the electromagnetic wave equation? Or is because superposition between quantum mechanical objects act kind of like waves? (bear with me, I'm not sure I understand my own question, I'm just an undergrad and I've only taken a modern physics course)

Look at the standard classical wave equation.

Now look at the time dependent Schrödinger equation. Both of them have similar structure.

Regardless of that, no one here should be hung up on such labels. If you do, you'll be tripped by the term "particles", "spin", "angular momentum", etc. Instead, understand the actual physics and use those labels simply as placeholders.

Zz.

 

[Amok]

Or is because superposition between quantum mechanical objects act kind of like waves?

I'd say yes. For historical reasons a lot of the terminology used in QM has to do with waves (wavefunction, DeBroglie wavelength), and there are some similarities between the concepts, but you can't push the analogy too far. I also think that the wave thing is used to mark the difference between the Schroedinger point of view and the Heisenberg point of view.

If you try to think of a wavefunction as some sort of wave in the classical sense you'll only get confused. Think of it as new physics (which is cool).

 

[nukeman]

Can anyone answer this?

If I have a molecule, or anything really (something very small)

If it vibrates... Are the quantum mechanical objects the molecule it self and the vibration and wave it gives off?

 

[Amok]

Are the quantum mechanical objects the molecule it self and the vibration and wave it gives off?

I don't understand your question. What's the wave it gives off? Read an intro to Schroedinger's equation and things will become clearer.

 

[JohnLuck]

Can anyone answer this?

If I have a molecule, or anything really (something very small)

If it vibrates... Are the quantum mechanical objects the molecule it self and the vibration and wave it gives off?

All particles interact with the world like particles, but if you want to know where it will move between interactions, you will have to calculate it as a wave of probability. That means that when you send an electron through a plate with two holes in it and it has an equal probability of going through either one, the probability wave of where the electron will hit the wall behind the plate, will be an interference pattern (look it up). This confuses people because interference patterns are something that only a multitude of particles can otherwise produce.

But these things we call particles are not really particles or waves, they are something very different that is hard to get an intuitive understanding of, because we can not observe them directly. The reason we call them particles or waves is because some of their characteristics resemble those at different times, but they are something that neither of those descriptions fully capture. And there is nothing strange about this in my opinion, there is no special reason to believe the phenomenons observed on the microscopic scales should be analogue to something on the macroscopic scales.

To answer you question more directly, everything is a quantum mechanical object.

 

[remnax]

Schrödingers equation is called a wave equation partly for historical reasons
(Schrödinger thought the equation he found would describe real waves) and
partly because it admits wave-like solutions in many situations. But the meaning
of these wave-like solutions is different from real waves (like sound waves): they
are probability waves. The molecules are real objects because you can 'see' them
but their positions cannot be determined by means of these solutions - to verify
a prediction of quantum theory you need many molecules or many repetitions of a
single experiment, In short quantum theory is a statistical theory (my opinion).

 

[Maui]

But these things we call particles are not really particles or waves, they are something very different that is hard to get an intuitive understanding of, because we can not observe them directly. The reason we call them particles or waves is because some of their characteristics resemble those at different times, but they are something that neither of those descriptions fully capture. And there is nothing strange about this in my opinion, there is no special reason to believe the phenomenons observed on the microscopic scales should be analogue to something on the macroscopic scales.

then the next paragraph makes no sense:

To answer you question more directly, everything is a quantum mechanical object.

as quantum mechanical 'objects' show demonstrably very different behavior and characteristics than everyday objects. QM makes no reference to objective reality as it's perceived and people looking for an explanation are guaranteed to be frustrated by the lack of support for such concepts. For almost a century there has been no place for something like a 'universe' and the term is now obsolete and replaced by 'reality' in virtually all of fundamental physics(this is an extention among the experts as fundamental physics also makes no mention of objective reality, except in some very speculative ways). There are unresolved metaphysical issues with the passage of time, history, dinosaur fossils, etc. but only through accepting the inevitable - that the universe is a reality - can the conceptual issues be resolved that plague the physics of the so-called objective reality theory. And this is not just backed up by some of the brightest scientists of the last century and experimental data, but is also understood and accepted by the majority of 'regular' quantum physicists. It took me close to 4 years to fully appreciate the meaning behind Bohr's statement "If you are not shocked by qm, you have not understood it". All it was meant to say is - "the 'universe' is a reality, there is no coming back, live with it". Note however that this isn't implying that reality is necessarily divine or supernatural but it does compel us to think in new ways about what is observed. To the OP:

But, I want understand a quantum wave function, mainly how you can describe a wave by the particle it self?

This is how the world works. At some level, the known classical world emerges out of probabilities represented by the wave in a similar way that color and taste emerge from the interaction of molecules.

 

[bhobba]

then the next paragraph makes no sense

Sorry mate but I see no problem at all. The fact of the mater what a quantum object is apart from when it is being observed is anyone's guess. I on occasion have been caught up in not being too careful about this saying things like a particle in a superposition of positions is literally in those positions simultaneously - but such descriptions are wrong and we all should try be be as careful and exact as possible when talking about QM.

Thanks
Bill

 

[bhobba]

But these things we call particles are not really particles or waves, they are something very different that is hard to get an intuitive understanding of, because we can not observe them directly. The reason we call them particles or waves is because some of their characteristics resemble those at different times, but they are something that neither of those descriptions fully capture. And there is nothing strange about this in my opinion, there is no special reason to believe the phenomenons observed on the microscopic scales should be analogue to something on the macroscopic scales.

Spot on IMHO

Thanks
Bill

 

[derek101]

Should I be thinking that the macroscopic world and It's laws of physics,emerge from a totally different set of physical laws of the microscopic quantum world.
Or is this the wrong approach?

 

[bhobba]

Yes.

Thanks
Bill

 

[Maui]

Sorry mate but I see no problem at all. The fact of the mater what a quantum object is apart from when it is being observed is anyone's guess. I on occasion have been caught up in not being too careful about this saying things like a particle in a superposition of positions is literally in those positions simultaneously - but such descriptions are wrong and we all should try be be as careful and exact as possible when talking about QM.

Thanks
Bill

Leaving aside conspiracy theories, if it walks like a duck, quacks like a duck, looks like a duck, it must be a duck.

Spot on IMHO

How is this spot on, when in the next paragraph he continues:

To answer you question more directly, everything is a quantum mechanical object.

There are no classical objects, there is classical-like behavior at observation/measurement, so the previous statement must clearly be wrong.

 

[HomogenousCow]

...it saddens me to see how this thread has turned out
Let me give you a quick run down of how nonrelavistic quantum theory works.
All systems are represented by states with "length" 1, these states encode everything you can know about the system, I stress the word CAN.
Observables are represented by linear operators which have real components (and other propetieis, referred to as hermitian operators)
The Schrödinger equation relates a state in the present to it's behavior in the future.
The state of the system projected in the position basis, is popularly known as the wave function, so this function really is just the coeffecient of the position vectors that it is being projected in (hmm components is a better word, whatever) . These are probability amplitude densities (impressive word eh?), so basically you just take the modulus square of the function and then integrate over a section of space, and ta-da you have the probability of finding the particle (or whichever one you are looking for, different particles in the system have their own position basi) in that section of space.

Nobody has any idea why this works, it just does.

 

[bhobba]

To answer you question more directly, everything is a quantum mechanical object.

There are no classical objects, there is classical-like behavior at observation/measurement, so the previous statement must clearly be wrong.

You keep alluding to some kind of inconsistency in what was written. There is none I can see - in fact it looks spot on. You may giving too deeper a meaning to 'quantum object' assuming it implies something real exists out there - I take it to mean the quantum state which is knowledge about a system - not something 'real'.

Thanks
Bill

 

[bhobba]

These are probability amplitude densities (impressive word eh?), so basically you just take the modulus square of the function and then integrate over a section of space, and ta-da you have the probability of finding the particle (or whichever one you are looking for, different particles in the system have their own position basi) in that section of space.

By using the word 'finding' you are suggesting its there and you are determining where it is - such is not the case in all interpretations. I think you probably didn't really mean to imply that - just pointing out sometimes the language we use in this area can have subtleties to it.

Thanks
Bill

 

[HomogenousCow]

Please stop arguing over petty semantics, the OP asked a question, answer it and leave.

 

[nanosiborg]

I understand a normal mechanical wave, simply a disturbance that moves.

But, I want understand a quantum wave function, mainly how you can describe a wave by the particle it self?

You can't. There are limits regarding what can be described using a particle formulation and what can be described using a wave formulation. Generally, the wave formulation describes pre-detection situations, and the particle formulation describes post-detection situations. The complementary relationship between the two is the basis of what's called the wave-particle duality in the orthodox or Copenhagen interpretation of the quantum theory. You might start with Heisenberg's "The Physical Principles of the Quantum Theory", and work forward from there.

Apparently, the nature underlying instrumental results has both wavelike and particlelike properties. The foundation of the old quantum theory is based on conceptualizations or inferences regarding visualizations of deep reality in terms of familiar notions of particles and waves in particulate media. However, modern quantum theory has become somewhat removed from these conceptualizations and the mathematical treatments of various instrumental phenomena have become abstract to the extent that they are less amenable to prior inferential conceptualizations.

So, how should one think about the Schrödinger equation, wavefunctions, etc.? Well, the only thing that's known for sure is that, so far, it's an effective way of modelling experimental preparations in terms of what might be called a probability mechanics. Any wavefunction, in qm, is a distribution of particulate amplitudes, the square of which is a predictor of probable instrumental (ie., particulate) results. Beyond that, regarding how it might relate to what's actually happening in the deep reality, is a matter of contentious speculation.

 

[bohm2]

Can anyone answer this? If I have a molecule, or anything really (something very small)If it vibrates... Are the quantum mechanical objects the molecule it self and the vibration and wave it gives off?

DeBroglie suggested this idea. He proposed that inside the particle there was a periodic process that was equivalent to an "internal clock". Thus, there was a physically ”real” particle that induces a physically relevant ”realistic” wave, and that wave in turn is capable of affecting further motion of the particle. This particle-wave association picture has been artificially induced (e.g. via external vibration frequency) on the macroscale by Couder's group:

Single-Particle Diffraction and Interference at a Macroscopic Scale
https://hekla.ipgp.fr/IMG/pdf/Couder-Fort_PRL_2006.pdf

Interestingly, there was a fairly recent paper suggesting some evidence for an internal clock:

A Search for the de Broglie Particle Internal Clock by Means of Electron Channeling
http://download.springer.com/static/pdf/840/art%253A10.1007%252Fs10701-008-9225-1.pdf?auth66=1354414412_9153bb19281c3647b32964776bdbd6a7&ext=.pdf

Physicists catch sight of trembling particle
http://physicsworld.com/cws/article/news/2010/jan/06/physicists-catch-sight-of-trembling-particle