EFFORTPOST Scientist tendie flinging drama on researchgate.

Dear Ulrich My answer is limited to the one, two, or three dimensional spatial space. Therefore, in momentum space, the dimension of the wave function is similar to the above, provided that the length is replaced by the linear momentum.

Ulrich becomes mildly annoyed and passive aggressively says:

OK, but all this is already expressed in the first contribution to this thread. Sometimes reading the precedent contributions is useful.

OP sees it devolving and intervenes.

Thanks for both of you Mr. Ulrich and Mr. Saeid. your reply is useful and appreciated.

It seems Dr. Mutze's bloodlust is interrupted for now and unfortunately we will be getting no more passive aggressiveness, condescension or rslurration from this thread anymore.

Luckily our journey doesn't end here. Himangshu Prabal Goswami of the Max Planck Institute for the Physics of Complex Systems (the first institution here that isn't a random no name) jumps in 4 days later to save the thread with an unironically r-slurred take:

The wave function does have dimensions, depending on what space you use to represent it. Say, the spherical polar co-ordinate system,eg. 1s=1/(sqrt[pi ao^3])Exp[-r/ao]. So its dimensions are L^(-3/2). You can reduce the dimensions as well.

It essentially comes from the interpretation of the wave-function. |Psi(q,t)|^2=1. So the volume element, dq, will determine the dimension and that will be reflected in the normalisation constant. Anyway, although wave-function is a very useful tool, I agree with lot of books which states, it has no physical meaning. That makes it useless to check its dimensions.

Ulrich immediately smells blood in the water:

Himangshu, the logic of physics is complicated enough that it is not always easy to express it unambiguously in our language. Saying that the wave function has no physical meaning may create a wrong impression for some readers. Saying that it has no direct physical meaning is more precise. Think of the four-vector potential A in electrodynamics. In the 19th century it was considered as a merely mathematical tool. Then quantum theory came and it turned out that A is the primary quantity that transmits electromagnetic interaction. So the indirect physical meaning changed into a direct one. Dimensions have to be right for formal consistency. The need for handling them correctly has noting to do with physical meaning. So your last sentence is strongly misleading.

Himangshu reveals he is a chemist. This explains everything and if for some incomprehensible reason you at all still cared what he had to say, you can safely know the opposite of anything he says is true.

Dear Harry and Ulrich, I agree to whatever you say. The wavefunction is indeed the most beautiful tool for a chemist. What I fail to comprehend is the utility of adding dimensions to particular quantity, which has no physical essence. Dimensions essentially as per as I believe is the conditional ability to add reality to its mathematical description so as to converge more in to the physical intuition, as in the vector potentials. To the wave function, till this date, association with reality has been denied/debated. Hence I made that statement. If you have an alternative and more convincing description, please free to rectify me. You guys have been into this field more than I have. And I will be happy to correct myself.

Some barges in 6 months later to semi-incoherently give an even worse answer than any answer given previously. Side note, his profile itself is rslurred:

I work on High Energy Physics theory. Standard model of particle physics, which is very well established today, has a fairly long list of unknown parameters. The number of unknown parameters is likely to increase once dark matter and dark energy problems are addressed.

Anyways, his contribution:

Actually it is a very good question.

Wikipedia says that

"For example, for a 3-dimensional wave function the amplitude

has a "bizarre" dimension [L^−3/2]."

Interesting point to note is that when you are solving an one

dimensional problem the probability amplitude has a

different dimension from what is quoted above. In a one

dimensional problem psi^2 dx is dimensionless so psi

has a dimension L^-1/2

In a two dimensional problem psi^2 dxdy has to be

dimensionless so psi has a dimension L^-1.

Luckily our protagonist is still monitoring the thread, passive aggression at the ready:

@Biswajoy

Actually not only the question is good. Good are also some answers. These render your's superfluous.

Ulrich: There is no harm in appreciating a good question or

a good answer. Many people might have identical thoughts.

I did not find a note in this thread which points to the fact that

the dimension of wave function depends on the type of problem

you are solving. Such as 1-D, 2-D or 3-D. This is a simple fact but

requires to be stressed specially for non-experts. That was the reason

behind my posting.

At this point this guy makes poor Ulrich miss even Saeid:

@Biswajoy

For your information: the second contribution (by Saeid Soheyli) gives the relation to space dimension explicitely.

Fast forward 4 years:

A few boring posts have happened but nothing interesting. Luckily a new lolcow has come to save the day, James Robinson:

szabo and ostlund - modern quantum chemistry, 1989, p42, wavefunction shown as a0^3/2, 2.5978E15 m^-3/2.

What did he mean by this?

Ulrich is on the case!

Dear James,

unless you tell us how a comma separated pair of values can stand for a wavefunction and whether m stands for a particle mass or for the SI unit of length your contribution makes no sense to me.

a0 is 0.52918 Angstroms (1 bohr if memory is correct) and the m is meters, there was a typing error, the conversion factor for psi to si units is a0^-3/2, which is 2.5978E15 and the units are meters^(-3/2). Apologies.

James,

in addition to the dimension (in 3-dimensional position space --- as opposed to momentum space) you also give numerical values. As far as dimension is concerned, many of the previous answers gave this already. Hopefully you are aware of the fact that the numerical value is irrelevant (or meaning-less) in the context of the original question.

At this point this r-slur deserves to be beat to death with a stick and if anything our protagonist goes too easy on him.

Hi Ulrich, I meant to provide a numerical simple example.

In a physics examination the professor pointed out of the window to the sky and asked the student: You see the clouds all around --- why they don't fall down, given that they consist of water which undoubtedly is heavier than air? The student plays for time and asks: Which of the many clouds do you refer to?

The idea that a 'simple numerical example' would enlighten any aspect of our question looks to me not more reasonable than this student's question.

Waleed Alawsey

Thanks for the question

To this day (a year ago) people are still occasionally giving worse variations of the same answers in this 9 year old thread.