Quantum numbers are the solutions of Schrodinger wave equation. These are the parameters, explaining the electron behaviour around the nucleus.
I saw the above in one of the videos about quantum numbers on YouTube.
What is the grammatical form and function of "explaining the...nucleus"?
Is it a reduced relative clause which modifies the noun "parameters"
Should there be a comma before that part?
I don't know exactly what you would call it - if "parameters" had been an object, one might call "explaining the electron behaviour around the nucleus" an object complement or an adjectival phrase modifying the object.
I suppose, in this sentence, I would call it "an adjectival participle phrase modifying 'parameters'".
I think that the comma is not really needed.
Possibly, part of the trouble is that different grammars explain things in different ways.
One might call this a reduced relative clause.
Another might say it's a "participle phrase".
Another would call it an "adjectival phrase".
Yet another might call it an "adjectival participle phrase".
I really prefer (for myself) to use "function grammar". This explains what a group of words DOES, not 'what form does it take'?
"explaining the electron behaviour around the nucleus" says something about parameters.
So, it is adjectival - it says something about a noun.
It doesn't have a finite verb, so it is not a clause, it's a phrase.
It's a phrase, and it modifies a noun, so it's an adjectival phrase.
I don't need to know "Did the writer originally think of the clause 'which are explaining the electron behaviour around the nucleus', and then shorten it by removing the pronoun and verb?"
It doesn't matter to me what the writer thought - what matters to me is what the sentence means.
If you need to (for the purposes of your course, or tests you will take and so on) explain the FORM of the phrase, then you need to ask your teacher/tutor for help.
Almost any phrase beginning with a participle, and which modifies or explains a noun, can be expanded into a relative clause.
The form of "reduced relative clauses" and "adjectival participle phrases" are identical in many cases. You could call them either.
I will bow to Drag0n's definition of the phrase. (It's Saturday morning and I've not yet had enough coffee.) I will, however, be far more definite on punctuation: The comma should not be there. It is incorrect.
The phrase "explaining the electron . . ." is not an optional aside and is not an independent clause. The comma is not needed to provide a breathing break for a speaker (which is a difficult thing to determine and is a legitimate reason for a comma). The comma does not increase the clarity of the sentence. (I.e. it doesn't make the sentence easier to understand.) In fact, the comma makes the sentence more difficult to understand.
These are the parameters which explain the electron behaviour around the nucleus.
Again, there is no comma. The last part of the sentence, in either of the versions, is an integral part of the meaning of the sentence. It cannot be removed without losing the meaning of the sentence. The underlined part of the second sentence of this paragraph is such extra information, not necessary to the meaning of the sentence (<<<as is that "not necessary . . ."). In this case (these cases) one is supposed to use a comma.
The comma should not be there. It is incorrect.
My "I think the comma is not really needed" was an understatement!