There are several "schools" of thinking about the motivations for using the atomic bombs on Japan during WWII. The "orthodox" approach was that put forward by the policymakers who made the decision, and became largely cemented in 1947 with an article by Secretary of War Stimson in Harper's magazine titled "The Decision to Use the Atomic Bomb." This is the one most people are familiar with: Truman weighed the options of a land invasion versus the use of the bombs, and decided (with a heavy heart etc.) to use the bombs to end the war. It is worth noting that the reason this was published in 1947 is because criticism of the use of the bombs was increasing in the USA, and this was meant to "redefine" the narrative in pretty much unassailable terms. If you accept the premise, that there were these two options, then the result is practically impossible to argue with.

There were, even at the time, alternative views, which would later be called the "revisionist" views. The first person to put forward the "intimidate the USSR" narrative in a major way was the British physicist P.M.S. Blackett, in "Fear, War, and the Bomb" (1949), which famously argued that "we may conclude that the dropping of atomic bombs was not so much the last military act of the second World War, as the first major operation of the cold diplomatic war with Russia now in progress." This was greatly expanded upon by later historians, notably Gar Alperovitz, in the 1980s and 1990s, using newly-declassified records. This view argues, as your professor apparently did, that the atomic bombs were known to be not necessary to end the war, and that the US deliberately used them in order to "send a message" to the USSR about the coming Cold War.

There are aspects to each view that are supportable by the documentation, and there are aspects to each view that are unsatisfactory. To be very brief about it: the problem with the "orthodox" view is that at no time is there any documentary evidence that makes it clear that it was such a simple "weighing" of options. Once the bomb was proven usable, there was practically no doubt in high levels of policy that it would be used. There were some questions about how it would be used — what kind of target, a city or a military base, for example (the result was "a city with a military base in it," something of a compromise of two different value systems). There were questions about whether the war could be averted diplomatically prior to use (more on that in a second), there were choices made about how "easy" surrendering could be made for Japan. And there was no foreknowledge that using a nuclear weapon, much less two (and I would note that while the first use of the bomb had a lot of planning involved in it, the decision to use the second bomb was more or less conducted by the military people on the island of Tinian, with no high-level input into it, and I suspect it was entirely a surprise to Truman, Stimson, and others when it was used), would end the war. The highest level personnel on the Manhattan Project which made the bombs thought it might take as many as five bombs and an invasion. "Invasion vs. bomb" was never, in other words, the choice: it was always bombs and invasion, and in fact the rapid surrender of Japan proved to be quite a surprise. (It is just worth noting that the invasion of Japan was not planned until November 1945, so there were several months before it would begin at the time the bombs were used; it was not an immediate dilemma.)

The "revisionist" view has some merits. For example, it is clear that Truman and his Secretary of State, James Byrnes, deliberately did not make it easy for Japan to surrender as they could. Stimson, Churchill, and many others including military intelligence, urged Truman to include a clause in the Potsdam Declaration that would make it clear that the US had no intention of harming or even deposing the Emperor. They wanted this clause because, based on intercepted and decrypted communications (known as "MAGIC"), they knew that the Japanese high command was split between the hardcore militarists who wanted to fight to the death (a "bleeding" strategy that was hoped to make the American public tire of war) and those in a "peace" faction who were seeking a diplomatic end to the war. They knew those in the "peace" faction were trying to get the then-neutral USSR to mediate a surrender agreement with the USA, and the main sticking point was the question of the status of the Emperor and the Royal House in the postwar. They argued that culturally it would be almost impossible to get the Japanese high command to agree on a situation of truly unconditional surrender, because of the Emperor question (and indeed, the only way it actually happened in reality is that the Emperor himself pushed for it; only one man, in the end, could really make that decision). So the "revisionist" view would say, see, they could have ended the war, but they deliberately (and there is no doubt that it was deliberate; it is easy to document) set things up in a way that would make it hard for Japan to surrender, with the idea that they could then use the atomic bombs.

The "revisionists" also point to some evidence that at least some of the American high command, notably Byrnes and sometimes Stimson, explicitly saw the use of the bomb as having relevance for their postwar relationships with Russia. There were some who did believe that it would be a "bargaining chip" and serve to buffer American interests against an ally who they increasingly saw as aggressive, untrustworthy, and expansionist in their goals. They were watching in horror as the USSR sapped democracy and free speech out of every country they occupied, turning them into puppets of the Stalinist state, and they quickly saw that once the common enemy was defeated, there would be little chance of an American-Soviet friendship lasting very long.

So the "revisionist" view is not crazy by any means. But it has its own problems. Like the "orthodox" view, it vastly overstates how much people thought they were capable of predicting the future — there were deep, legitimate uncertainties about the best way to end the war, and the decisions on the use of the bomb were not as carefully-considered or well-considered as either view makes them out to be. Again, they had a bomb, it was assumed they would use it — there was an aspect of the entire operation as a train running on rails that had been put in place years earlier under Roosevelt, and nobody, including Truman, had strong reasons for trying to derail that train.

And while it is true that the foreign policy aspects of the bomb were one of the "motivations" that some people had for using it, it should be noted that there were many people involved in this work, and they had multiple motivations. In some sense the use of the bomb was "overdetermined" — there were so many "good" reasons to use it in their view, and so few reasons to not use it. In some sense, to use it was the "easy" path: they already had spent billions on it, they were using it against an admittedly terrible enemy whose own war fighting gave no consideration to the lives of non-combatants, it would shore up the US military position going forward (including with respects to Stalin), and maybe (who knows?) it would end the war earlier than it would otherwise. (Some of the scientists who worked on the project had another motivation for using it: better to use the first generation of nuclear weapons in a horrific way now, and to establish a desire to control nuclear arms as a result, than to let them become mere weapons of a future war. They knew what most people did not: that the next generation of weapons could easily be a thousand times more powerful, and would be deliverable in minutes from un-blockable missiles.)

Why wouldn't you want to use them? To save civilian lives? While there were some, even at the high levels of US government, who were concerned about wanton slaughter of civilians (Stimson cautioned Truman that the firebombing raids on Tokyo would give the US the reputation of "outdoing Hitler in atrocities" if they continued), this was not a primary concern for that war, as evidenced in many other actions by the United States and the Japanese. That moral line, in other words, had long since been passed. Another reason given, by some of the scientists on the bomb project, was that the world might come to fear the United States as a "nascent Germany" and believe it had global imperial ambitions (and, in a sense, it did) — this argument was not at all successful on the policymakers, who thought, if they even heard it (it never made it to Truman), that it was idealistic and naive about how politics worked on a global scale (and what expertise do physicists have about international politics, anyway).

There is a middle-ground view, what the historian J. Samuel Walker calls the "consensus view," on the bombings, which is more like what I have been expressing in my own reply here: that there is a synthesis of sorts of the "orthodox" and "revisionist" views that recognizes how "messy" the situation was, how "grand strategy" was only a minor component in the overall operation, and that recognizes that the use of the atomic bomb was only one component out of many others going through the minds of the policymakers at the Potsdam Conference, when the final bombing order (formally approved by Stimson, not Truman, as an aside!) was sent issued. It is, I think, the more correct view, even though it is unsatisfying to many people who read of it today, because it does not fit into any simple modern-day political narrative about heroes and villains, or about rationality and strategy. But it seems to match the contemporary documents much better, and seems to match what we know about human beings and human organizations much better.

First of all, the view that Japan was about to surrender was a minority position held by a few analysts at the time, but not supported by the majority. Many other sources indicated that the Japanese were preparing to resist the land invasion of mainland Japan with extensive force, and the capture of Japanese documents after the war further supported this belief. Captured internal communications between Japanese generals showed that they believed that if they could sacrifice 20 million lives in kamikaze efforts then "victory will be ours". Also, the Japanese mainland defense plan at the time (Ketsu-Go) involved mobilizing all men ages 15 to 60, and all women ages 17 to 40 to fight off US ground troops with wooden spears, swords, and sticks of dynamite. The whole goal was to force the US to give up the war because it could not support a successful campaign in the face of excessive casualties.

Furthermore, there is no historical documentation from the time that indicates that policy makers were at all considering the move as a means of "scaring the USSR." Not only is there no documentation of this thought process, but other actions by the US contradict this theory. For example, the US engaged in significant lend-lease operations with the Soviet Union throughout World War II (over 400,000 jeeps and trucks; 12,000 armored vehicles (including 7,000 tanks); 11,400 aircraft and 1.75 million tons of food. source: Wikipedia for those interested). What's most important to your question is that these shipments of supplies and food didn't stop until September 20, 1945, more than a month after the Japanese surrendered, and many months after it had become clear that Germany was going to fall.

Now, if US policy makers were seriously considering the USSR as a strategic threat, why would they continue to give billions of dollars of supplies to the Soviets months after it was clear that the war in Germany was effectively decided? Why would they continue to aid the Russian push into Europe (thus putting more territory under Soviet influence) by continuing to supply trucks, planes and tanks to the Soviet army? If war with the USSR was a serious concern of the upper levels of the US government, then why continue to provide tanks and planes to an army they thought they were about to fight? Especially months after it was no longer necessary to do so? Surely not to convince them to fight against Japan, as the USSR's involvement in the war was at best a token gesture which didn't occur until two days afterthe first atomic bomb was dropped on Hiroshima.

Furthermore, these claims seriously underestimate the extensive cost of the Manhattan project, and the effect that had on the weapon's use. The Brookings Institute estimates the effective cost of each nuclear weapon at approximately $5 billion each (in 1996 dollars). To put that in perspective, the US only spent $24 billion on guns. So, using 3 of the 4 bombs the US had produced up to that point was the monetary equivalent of expending 62% of all the money spent on all guns given to soldiers in the entire US army. The idea of expending that amount of money to maybe scare the USSR (who was a strong ally at the time, and about to declare war on Japan in support of the planned US invasion) is more than a little silly.

Furthermore, the idea that the US would expend fully two-thirds of it's remaining bombs to scare the USSR with a weapon that it could not effectively use more than one more time is to suggest an incredible level of strategic incompetence. A single nuclear bomb, even dropped on Moscow, would not have had a crippling effect on any war between the USSR and the US. There's also the fact that successfully using an atomic bomb at the time required the ability to fly a bomber directly over the target, which was incredibly difficult to do in the face of any significant enemy air power, and was only employed against Japan because their air force had been virtually eliminated by that point in the war. The USSR was in no such situation (due in no small part to the thousands of planes the US had given them), and so dropping our one remaining bomb on any significant Russian city would have been virtually impossible.

Overall, there's little to no historical evidence to support the idea that the atomic bombings of Japan were conducted with any purpose other than ending the war with Japan as quickly as possible, and there's significant evidence which points to rational holes in that argument.