Why does Obi-Wan not mention Qui-Gon Jin in the original trilogy? After all, Qui-Gon was his master. At the end of the prequel trilogy, Yoda said that he was going to teach Obi-Wan to communicate with Qui-Qon. Unfortunately, Liam Neeson could not make an appearance in "Revenge of the Sith" as planned due to a motorcycle accident.

Well since the first saga was made first (IV- VI) they didn't even know about Qui-Gon. The reason yoda had mentioned Qui-Gon at the end of episode 3 was because from episode I-III no one had been able to know how to communicate with the dead, and during episode IV Obi wan communicates with Luke. So for episode III, they wanted a way to explain how communicating with the dead first was learned.

You fail to see my point. That is probably bad planning on behalf of George Lucas. Also, Luke was not dead so really, Obi-Wan's communicating with Luke is unrelated.

first was episode 4.if you remember, in episode 5: "go to the dagobah sistem and find master yoda, the jedi master who instructed me"
GL's first ideea was that yoda was obi'wans master
after epsiode 6, GL wanted to show how good was obi-wan, since in the first trilogy...he wasn't sooo impresionating.so that's wy qui-gon died.but obi-wan did kill maul
if yoda would be his master, it would be no really big adventure for, obi-wan....yoda was a milion times better than maul, he would kill him in two minutes or less
and maul couldn't kill yoda because yoda died in episode 6.

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"Obi-Wan is a great mentor, as wise as Master Yoda, and as powerful as Master Windu."
―Anakin Skywalker

The real explanation is that Quiggy wasn't thought of until Episode I. But for a canonical explanation, Yoda had a very big influence on all the Jedi of that age, and instructed most of them. Besides, Yoda was the only other Jedi who survived Order 66 (Besides the others that went rogue). It wouldn't do Luke any good if Obi-Wan told him about Qui-Gon.