Die Professorin sagt, wir sollen nur Quellen zitieren, die wir in der Fußnote genau angeben können.

Die Professorin is the subject of the sentence, so it is in the nominative case.

A few useful details:

• Professorin is the feminine form of Professor
• the article die here is feminine singular nominative
• this die is different from the later die in the sentence

So here, Die Professorin simply means the person doing the speaking.

The comma separates the first clause from the clause that reports what the professor says.

German often does this with verbs like:

• sagen
• denken
• glauben
• wissen

Here you have:

• Die Professorin sagt, ...

Then comes the content of what she says:

• wir sollen nur Quellen zitieren ...

You could also say:

• Die Professorin sagt, dass wir nur Quellen zitieren sollen ...

That version uses dass. In your sentence, dass is simply omitted.

Because German often allows a reported statement after verbs like sagen without using dass.

So both of these are possible:

• Die Professorin sagt, wir sollen nur Quellen zitieren ...
• Die Professorin sagt, dass wir nur Quellen zitieren sollen ...

The difference is mostly in structure:

• without dass: the next clause keeps normal main-clause word order
  
  • wir sollen ...
• with dass: the verb goes to the end
  
  • dass wir ... zitieren sollen

Both are natural.

Here sollen means something like:

• should
• are supposed to
• are expected to

It often expresses an instruction, expectation, or recommendation that comes from someone else.

So in this sentence, it is not just a general idea of should. It specifically reflects what the professor says is expected.

Compare:

• Wir sollen nur Quellen zitieren. = We are supposed to cite only sources.
• Wir müssen nur Quellen zitieren. = We must cite only sources.
  This sounds stronger, more like necessity.
• Wir wollen nur Quellen zitieren. = We want to cite only sources.
  This expresses intention, not obligation.

Because sollen is a modal verb, and modal verbs usually take another verb in the infinitive.

In the clause:

• wir sollen nur Quellen zitieren

the parts are:

• wir = subject
• sollen = conjugated modal verb
• zitieren = infinitive

In a main clause, the conjugated verb goes in second position, and the infinitive usually goes to the end.

So:

• Wir sollen ... zitieren.

not:

• Wir sollen ... zitierenen or any other conjugated form

Because German often uses a bare plural when speaking about things in a general sense.

So:

• nur Quellen zitieren = cite only sources

This means sources in general, not a specific set already identified.

Compare:

• nur Quellen zitieren = only cite sources
• nur die Quellen zitieren = only cite the sources
  This would mean specific sources already known from the context

So the lack of an article is completely normal here.

This die is a relative pronoun. It refers back to Quellen.

So:

• Quellen = sources
• die = that / which

The relative clause is:

• die wir in der Fußnote genau angeben können

It describes which sources are meant:

• the sources that we can specify exactly in the footnote

Grammatically, this die is accusative plural, because it is the object of angeben.

You can see that from the clause:

• wir = subject
• die = object

If you turn it into a simple main clause, it becomes clearer:

• Wir können die Quellen in der Fußnote genau angeben.

Because relative clauses are a type of subordinate clause, and in German subordinate clauses send the conjugated verb to the end.

The relative clause is:

• die wir in der Fußnote genau angeben können

Its structure is roughly:

• die = relative pronoun
• wir = subject
• in der Fußnote = prepositional phrase
• genau = adverb
• angeben = infinitive
• können = conjugated modal verb, placed at the end

That final position of können is normal for subordinate clauses.

If this were a main clause, it would look like:

• Wir können die Quellen in der Fußnote genau angeben.

Because in can take either dative or accusative, depending on whether it expresses:

• location → dative
• movement toward a destination → accusative

Here it means location:

• in der Fußnote = in the footnote

There is no movement, so German uses the dative.

Also:

• Fußnote is feminine
• dative singular of die Fußnote is der Fußnote

So:

• in der Fußnote = correct

Because angeben is a separable verb, and separable verbs only split in certain situations.

In a main clause with a finite form, it splits:

• Wir geben die Quellen genau an.

But in an infinitive, it stays together:

• Wir können die Quellen genau angeben.

And in your sentence, it is an infinitive because it follows the modal verb können:

• ... die wir in der Fußnote genau angeben können

So angeben remains one unit.

Here genau angeben means something like:

• state precisely
• give exactly
• specify accurately

In academic German, eine Quelle angeben often means to provide the source information properly.

So:

• Quellen genau angeben = to cite/specify sources accurately and completely

That fits well with in der Fußnote, because the idea is that the source should be detailed enough to be properly identified in a footnote.

They mark two different boundaries.

1. Die Professorin sagt, wir sollen ...
   This comma separates the reporting clause from what is being reported.

2. ... nur Quellen zitieren, die wir ... können.
   This comma introduces the relative clause describing Quellen.

The second comma is especially important because in German, relative clauses are set off by commas mandatorily.

So the punctuation is not optional here; it reflects the grammar of the sentence.