[hamdani yusuf]

I'm curious what should we interpret these things :
1. What kind of experiment is best represented by this animation.

The best I can find is evanescent wave coupling.
https://en.m.wikipedia.org/wiki/Evanescent_field
I've made my own experiment demonstrating this using microwave frequency a few years ago.

[Eternal Student]

Hi again.

Well these are all good questions from @hamdani yusuf .
   I'm going to try and rush through some answers.

1. What kind of experiment is best represented by this animation.

   I would imagine the animation was obtained purely on calculation from the Schrodinger wave equation and isn't based on any experiment.
    There are numerous experiments that seem to demonstrate quantum tunneling in operation.   The first thing that comes to mind are all the Scanning Tunneling Microsocopes  (STM) that are in use.   If you were just after hard evidence that it works in practice then I would start by Googling that.   Someone else has also mentioned electronic components like transistors.   I've previously linked to an article in Scientific American that describe some experiments including who did what, where and when so that you could find the original research papers if you were inclined.   I'm not really much of an experimentalist myself (you might have noticed).   STM 's - they work, they're good and they are the state-of-the-art application of Quantum tunneling.

 

2. The amplitude of the wave packet.

    Basically higher amplitude represents an increased probability of finding the particle there.   The probability of finding a particle at a given place and time is proportional to the SQUARE of the magnitude of the wave function, ψ.    It's conventional to just multiply the amplitude by a constant so as to "normalise" the wave function.  So there's nothing really special about the amplitude, it doesn't represent how much Energy the particle had or anything like that.  It's been deliberately scaled up or down to "normalise" the wave function.
   For a normalised wave function we have the relationship that |ψ(x,t)|² is precisely equal to (not just proportional to) the probability of finding the particle at position x and time t.     

3. The distinction between the real part and imaginary part of the wave function (psi).

     Surface level answer:   Not much.
     Medium level answer:   There are books and YT videos that discuss how and why complex numbers are important in QM.   There are some arguments that QM only works provided the wave function is complex valued and that this also provides some evidence for the existance of complex numbers in nature.   Personally, I think that's a ridiculuous  set of arguments.
     High level answer:   You're going to need another thread.

   

4. The 90 degrees phase difference between the real part and imaginary part of the wave function (psi).

    Provided the potential V is just a function of position and doesn't vary with time then you get solutions to Schrodingers wave equation that are separable or break into two easy parts:  A time dependant component T(t) and a space dependant component φ(x).    The over-all wave function is the product of the two  ψ(x,t) = T(t) . φ(x).    The thing that makes the wave function look like it waves up and down as time passes is of course the time dependant component T(t).
    That time dependant component T(t) will be of the form  e ^iωt  because Schrodinger's wave equation produces an ODE  (in the time derivative) with constant coefficients.    Applying  Euler's formula you get  e^iωt =  Cos ωt  + i . Sin ωt.    Now Sine and Cosine are 90 degrees out of phase so most of the complex solutions you generate will have real and imaginary parts that have time dependance like  Cosine  and  Sine  repectively.
   If you want to look harder and see if there's some deeper significance then we can.  I'll try and sketch some ideas here:

    As previously mentioned you can scale the wave function with an arbitrary complex number (indeed we MUST do this to normalise the wave function).  So we can multiply ψ by the complex number  Cos β + i. Sin β  for arbitrary angle β since all this will do is rotate it through the angle β in the complex plane without changing its magnitude.   So there's no significance in the actual phase of either the real or the imaginary part on their own, you can shift that phase as you please.  If there's anything interesting about the phase then it could only be the difference in phase that is of any interest or represents any important property.   
     There's not a great need to attach some importance to this phase difference because the magnitude of the complex number, ψ, already has an established significance.  We already pay a lot of attention to what the overall magnitude of ψ is doing and how that varies with time.   If one of the components, say the real part, was showing a rapid oscillation with time then there really isn't a lot of choice about how the imaginary part must oscillate unless we do also see an equivalent rate of oscillation in the overall magnitude of ψ.
      I don't know how familiar you are with complex numbers and I'm going to guess that no one wants to see a lot of mathematics here.  So unless you're really keen to discuss it further I'll just skip to the conclusion:  The phase difference is locked at 90 degrees because that's the only way that you could get rapid oscilliations in either of the real or imaginary part without observing some equally rapid oscillation in the overall magnitude of ψ.
   
   

5. The difference between positive phase and negative phase of the wave function (psi).

   ... see comments above...   you can rotate the wave function so that you have total freedom to decide if the real or imaginary part is considered to be leading the other one.

6. The number of waves in the wave packet.

   See details in the Wikipedia page or similar information about "generalised wave packets".   See Page 38 of   Quantum Mechanics by Franz Schwabl,  if by any chance you had the same book as the one I was reading.   
   In summary, I don't think it's all that important and this post is already too long.   All that was important is that you could see some waves.  If they (Wikipedia) had tried to construct an even more localised (shorter in space) wave packet or else given the oscillations a longer wavelength by adjusting the Energy, E, so that there were less wave peaks and troughs visible then you wouldn't have seen things as easily in the animations.    The number of wave peaks is determined by those things (localisation of the wave packet and Energy E).

Best Wishes.

Oops.  I can see I've overlapped with a reply from Hamdani.  I don't have any more time to spare, sorry, I'll just hope some of this was useful for now.

[hamdani yusuf]

I would imagine the animation was obtained purely on calculation from the Schrodinger wave equation and isn't based on any experiment.

The follow up questions are then:
- Is the animation a correct representation of Schrodinger wave equation?
- What does the animation try to achieve? Does it simplify the process, e.g. by removing distracting parameters, just like ignoring air resistance to calculate the trajectory of a cannon ball?
- Does it act as analogy by replacing an abstract concept with a more familiar concept, like analogy of electrical current using water flow?
- Does it help us to make a correct prediction of an experimental result?
If none of the above is true, I'm afraid that the animation will only add obstacles for those who try to understand the subject by creating a false conviction of knowledge.

AFAIK, even Schrodinger disagreed with Max Born on how to interpret the value of ψ.

[Eternal Student]

Hi again.

Is the animation a correct representation of Schrodinger wave equation?

   No.  Only of one one consequence of the wave equation (tunneling through a square walled barrier).

What does the animation try to achieve? Does it simplify the process, e.g. by removing distracting parameters, just like ignoring air resistance to calculate the trajectory of a cannon ball?

   It shows how a simple wave packet evolves when it is incident on a barrier.  It's animated so that temporal changes are shown in real time not in some static graph of something vs. time.
   Does it simplify?  Not much, I think -  but I didn't make it so I wouldn't be sure.  Wikipedia made it or someone made it and Wiki acquired it.    However, it's already been mentioned that most real life potentials aren't square walled, they may be steep hills but you would usually expect them to be smooth functions not step functions.

   

Does it act as analogy by replacing an abstract concept with a more familiar concept, like analogy of electrical current using water flow?

   No, it's still fairly abstract.  It's not an attempt to explain something in some different way.   It's more like just drawing a graph to show a function like y= x²  (because you could use words to describe the behaviour of y=x² but drawing a graph is a better way to show it).    This graph is animated so the values can be shown changing in real time.   The Real and Imaginary part of the wave function shown are the values you get from the solution of the Schrodinger wave equation with that potential.     (Don't get me wrong, I didn't make the animation.  Overall it looks right and matches diagrams in books but this one is animated so it moves.  I haven't checked any values to be honest.   They might have deliberately fudged a few values up or down a bit to make the animation a bit smoother or some other thing).

Does it help us to make a correct prediction of an experimental result?

    Well, it helped me and I would have thought it's useful for other people.  If it helps a person understand then they are much more likely to use the theory correctly.    You might be confusing "the animation" with the general theory, the animation isn't the theory it's just one graphical representation of one set of results for one situation.  It's representative of what happens in similar situations but that is all.
     You can't change the parameters like the potential barrier height in the animation - it's a demonstration not an online calculator.   Colin2B gave links to an online calculator earlier, there you can enter your own parameters and the appropriate results will be calculated.
    If you meant is the general effect known as quantum tunneling useful and does it make predictions:  Yes to the first - it's what inspired the creation of Scanning Tunneling microscopes and it does seem to explain how and why they work.   Yes to the second, you can make predictions and they can be tested.   For example there are some structures like long chains of Gold atoms that have been studied under an STM.   You can model the behaviour of the valence electrons in the gold chain quite well with just a 1-dimensional solution to the Schrodinger equation where the gold chain is effectively "the box" ( an infinite height square walled potential well).   You get solutions for the electrons in various different states.  In the n=2 state you should have a node (a region of constant 0 valued wave function) right in the centre of the gold chain.  Using the general theory of tunneling you should then detect the smallest current flow of electrons from the metal chain to the tip of the scanning micro socope when the tip is precisely over the centre of the chain.  When you do the experiment, that is what you find.

AFAIK, even Schrodinger disagreed with Max Born on how to interpret the value of ψ.

     This is true.  Quantum mechanics is bizarre and it's frequently said that no one understands it.   The Quantum tunnelling effect is just something you get by doing the calculations and seeing what the consequences will be.   It's not necessary to understand what ψ represents on some deeper level, or why the wave-function collapse happens, or any of the mysteries and controversies that are frequently attributed to QM.    Quantum tunneling just requires you to accept the axioms of QM and calculate.

Best Wishes.

[Eternal Student]

Hi again.

The best I can find is evanescent wave coupling.
https://en.m.wikipedia.org/wiki/Evanescent_field
I've made my own experiment demonstrating this using microwave frequency a few years ago.

    I can see your interested in performing experiments.    I've now spent some time trying to find an experiment that might be achievable at home with limited equipment.

    One of the cheapest and most readily available sources of quantum particles is light, you can get it out of a window although a torchlight or better still a laser pointer device would be better for this experiment.   You might be able to do something similar with your microwave genrator but you'll have more trouble "seeing" it, with light you should just be able to see it happening.
    The general idea is to fire a beam of light through a medium so that you observe total internal reflection at the boundary of that medium.  The light wave should have gone evanescent just outside that medium where it was incident on the boundary.   Your going to try and get that to re-enter another block of the same medium before the wave amplitude has dropped off too much, if it works then an ordinary travelling light wave should be re-established in the second block    (although with much lower amplitude than in the first block).   So, all this is going to involve is having two blocks of glass and trying to put them very close to each other.
    I found the details on page 149~150 of  An introduction to modern Astrophysics,  Carroll and Ostlie, 2nd edition, 2014.     I've attached a picture of the relevant section from that book.

Best Wishes.